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Why does Infiniti concept for professional mathematicians represent the hen
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bassam king karzeddin
2017-05-23 11:28:32 UTC
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Maybe the question is long enough to appear in the question title, so here it is again

Why does Infinity concept represent the hen that bleaches daily gold eggs for professional mathematicians?

Also, infinity was proven as a junk concept and mainly from its basic definition being unreal in terms of numbers and also being greater than any number, where this type of a definition sounds so crazy and a kind of hallucination really? wonder!

However, the existence which matters a lot in this whole story, where reality basically means existence

So, assuming for a while that concept of infinity is a nonsense concept, then many established facts, theorems, formulas, ... etc in mathematics would immediately be naked and unprotected where it collapses to doubtful untrue and absolutely wrong results for sure
So, what are the immediate subsequences that you might be able to logically conclude if you once drop this doubtful concept say for a while?

Regards
Bassam King Karzeddin
May 23, 2017
Me
2017-05-23 13:04:36 UTC
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Post by bassam king karzeddin
Why does Infinity concept represent the hen that bleaches daily gold eggs
for professional mathematicians?
Well, due to Hermann Weyl mathematics is

«die Wissenschaft vom Unendlichen» (the science of the infinite).
bassam king karzeddin
2017-05-30 10:33:47 UTC
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Post by bassam king karzeddin
Maybe the question is long enough to appear in the question title, so here it is again
Why does Infinity concept represent the hen that bleaches daily gold eggs for professional mathematicians?
Also, infinity was proven as a junk concept and mainly from its basic definition being unreal in terms of numbers and also being greater than any number, where this type of a definition sounds so crazy and a kind of hallucination really? wonder!
However, the existence which matters a lot in this whole story, where reality basically means existence
So, assuming for a while that concept of infinity is a nonsense concept, then many established facts, theorems, formulas, ... etc in mathematics would immediately be naked and unprotected where it collapses to doubtful untrue and absolutely wrong results for sure
So, what are the immediate subsequences that you might be able to logically conclude if you once drop this doubtful concept say for a while?
Regards
Bassam King Karzeddin
May 23, 2017
Now can you imagine how would the current or the modern mathematics look like if such a business concept was not adopted (as if it is truly any real or meaningful concept)

BKK
bassam king karzeddin
2017-06-07 12:09:27 UTC
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Post by bassam king karzeddin
Post by bassam king karzeddin
Maybe the question is long enough to appear in the question title, so here it is again
Why does Infinity concept represent the hen that bleaches daily gold eggs for professional mathematicians?
Also, infinity was proven as a junk concept and mainly from its basic definition being unreal in terms of numbers and also being greater than any number, where this type of a definition sounds so crazy and a kind of hallucination really? wonder!
However, the existence which matters a lot in this whole story, where reality basically means existence
So, assuming for a while that concept of infinity is a nonsense concept, then many established facts, theorems, formulas, ... etc in mathematics would immediately be naked and unprotected where it collapses to doubtful untrue and absolutely wrong results for sure
So, what are the immediate subsequences that you might be able to logically conclude if you once drop this doubtful concept say for a while?
Regards
Bassam King Karzeddin
May 23, 2017
Now can you imagine how would the current or the modern mathematics look like if such a business concept was not adopted (as if it is truly any real or meaningful concept)
BKK
Naturally, even the correct imagination is not allowed in mathematics, since it uncovers the so bad imagination immediately for sure

BKK
Markus Klyver
2017-06-07 17:53:49 UTC
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What's the nonsense about an element with certain properties?
bassam king karzeddin
2017-06-15 08:22:13 UTC
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Post by Markus Klyver
What's the nonsense about an element with certain properties?
In short, I have integer numbers greater than your infinity, wonder!

and your infinity is quite meaningless for more than sure

Hint: my posts

BKK
Markus Klyver
2017-06-15 08:28:22 UTC
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That's actually against the definition of what an integer is. But sure, you can declare the existence of multiple infinities if you like.
bassam king karzeddin
2017-07-10 12:33:15 UTC
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Post by Markus Klyver
That's actually against the definition of what an integer is. But sure, you can declare the existence of multiple infinities if you like.
I remember that I wrote about this issue at Quora, where If we have to accept this infinity concept, then and without loss of generality the air thematic rules must be changed, where this is also would not solve any big puzzle

New rules (say only in positive sense since this can be easily extended to negative sense, where then you fall into infinite number of distinct infinities, where then there isn't any larger infinity, that would immediately invalidate its current existing concept

To explain it in integers first, and in any chosen integer base number system, then there are the known infinities with an endlessly repeated model such as (142857142857142857.....), and there are the unknown random digits infinities such as (2564897364....), or digits of (Pi), or (e), or sqrt(2)

Where then, every unique representation of endless sequence of digits must represent distinct unique infinity

But this is not at all helpful in finding exact solutions, but APPROXIMATION as we do know and practice

for illustration:
[6/7 = 6*10^n/7*10^n] =/= [(6*10^n - 1)/7*10) = 0.857142857142...], when (n) is becoming with infinite sequence of integer digits, sure

Thus (1/7 =/= 0.857142857142...), since the first is well defined but the endless representation is a symptom of a number that tries always and hopelessly to replace or equate the original fraction, but always and forever unsuccessfully, thus not any real number for sure

And since numbers are unique in digital representation, prime factorization and also Geometric reprsentations

You may imagine it as a ghost number that is very good for comparison

Another solid many time repeated example that implies infinity concept would never help in creating the real existence of a solution to unsolvable Diaophnintin equations

Consider the simple Diophantine insolvable equation (n^p = 2m^p),

where (p > 2) is a prime number, (n, m, k) are positive integers, where no solution exists in the whole set of positive integers, but what magicians mathematicians usually do plough, by finding large integers for (n, m) for the actually different Diophantine equation of this form: (n^p = 2m^p + k), where (k) is relatively negligible integer in comparison with large (n, m)

And give you always and forever a long RATIONAL solution (in decimal form), since there is no other way

Or the divide the original unsolvable equation as (n/m)^p = x^p = 2), hence the solution (x = n/m = 2^{1/p}), but the shame is so obvious even to any clever school student that is only an approximations that they MUST confess so openly and so loudly,

Also, remember that 2^{1/p), for odd prime (p) is not constructible number, but again can be calculated or CONSTRUCTED as an APPROXIMATION ONLY

The theme is that infinity can't produce any new theorems but fictions only, especially that is only understood by its own so funny definition being unreal number but greater than any number (so funny indeed)

There are many more clearer proofs than this fast one in my posts for sure

BKK
b***@gmail.com
2017-07-10 12:54:47 UTC
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How can an approximation be wrong, think about it?
Why should an approximation be a fiction?

For example:

3 + 10/71 < pi < 3 + 10/70

is neither wrong nor fiction. To compute with approximation
use some interval arthmetic, you will see

whether you need a better approximation.
Post by bassam king karzeddin
Post by Markus Klyver
That's actually against the definition of what an integer is. But sure, you can declare the existence of multiple infinities if you like.
I remember that I wrote about this issue at Quora, where If we have to accept this infinity concept, then and without loss of generality the air thematic rules must be changed, where this is also would not solve any big puzzle
New rules (say only in positive sense since this can be easily extended to negative sense, where then you fall into infinite number of distinct infinities, where then there isn't any larger infinity, that would immediately invalidate its current existing concept
To explain it in integers first, and in any chosen integer base number system, then there are the known infinities with an endlessly repeated model such as (142857142857142857.....), and there are the unknown random digits infinities such as (2564897364....), or digits of (Pi), or (e), or sqrt(2)
Where then, every unique representation of endless sequence of digits must represent distinct unique infinity
But this is not at all helpful in finding exact solutions, but APPROXIMATION as we do know and practice
[6/7 = 6*10^n/7*10^n] =/= [(6*10^n - 1)/7*10) = 0.857142857142...], when (n) is becoming with infinite sequence of integer digits, sure
Thus (1/7 =/= 0.857142857142...), since the first is well defined but the endless representation is a symptom of a number that tries always and hopelessly to replace or equate the original fraction, but always and forever unsuccessfully, thus not any real number for sure
And since numbers are unique in digital representation, prime factorization and also Geometric reprsentations
You may imagine it as a ghost number that is very good for comparison
Another solid many time repeated example that implies infinity concept would never help in creating the real existence of a solution to unsolvable Diaophnintin equations
Consider the simple Diophantine insolvable equation (n^p = 2m^p),
where (p > 2) is a prime number, (n, m, k) are positive integers, where no solution exists in the whole set of positive integers, but what magicians mathematicians usually do plough, by finding large integers for (n, m) for the actually different Diophantine equation of this form: (n^p = 2m^p + k), where (k) is relatively negligible integer in comparison with large (n, m)
And give you always and forever a long RATIONAL solution (in decimal form), since there is no other way
Or the divide the original unsolvable equation as (n/m)^p = x^p = 2), hence the solution (x = n/m = 2^{1/p}), but the shame is so obvious even to any clever school student that is only an approximations that they MUST confess so openly and so loudly,
Also, remember that 2^{1/p), for odd prime (p) is not constructible number, but again can be calculated or CONSTRUCTED as an APPROXIMATION ONLY
The theme is that infinity can't produce any new theorems but fictions only, especially that is only understood by its own so funny definition being unreal number but greater than any number (so funny indeed)
There are many more clearer proofs than this fast one in my posts for sure
BKK
bassam king karzeddin
2017-07-10 13:58:10 UTC
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Post by b***@gmail.com
How can an approximation be wrong, think about it?
Why should an approximation be a fiction?
3 + 10/71 < pi < 3 + 10/70
is neither wrong nor fiction. To compute with approximation
use some interval arthmetic, you will see
whether you need a better approximation.
Post by bassam king karzeddin
Post by Markus Klyver
That's actually against the definition of what an integer is. But sure, you can declare the existence of multiple infinities if you like.
I remember that I wrote about this issue at Quora, where If we have to accept this infinity concept, then and without loss of generality the air thematic rules must be changed, where this is also would not solve any big puzzle
New rules (say only in positive sense since this can be easily extended to negative sense, where then you fall into infinite number of distinct infinities, where then there isn't any larger infinity, that would immediately invalidate its current existing concept
To explain it in integers first, and in any chosen integer base number system, then there are the known infinities with an endlessly repeated model such as (142857142857142857.....), and there are the unknown random digits infinities such as (2564897364....), or digits of (Pi), or (e), or sqrt(2)
Where then, every unique representation of endless sequence of digits must represent distinct unique infinity
But this is not at all helpful in finding exact solutions, but APPROXIMATION as we do know and practice
[6/7 = 6*10^n/7*10^n] =/= [(6*10^n - 1)/7*10) = 0.857142857142...], when (n) is becoming with infinite sequence of integer digits, sure
Thus (1/7 =/= 0.857142857142...), since the first is well defined but the endless representation is a symptom of a number that tries always and hopelessly to replace or equate the original fraction, but always and forever unsuccessfully, thus not any real number for sure
And since numbers are unique in digital representation, prime factorization and also Geometric reprsentations
You may imagine it as a ghost number that is very good for comparison
Another solid many time repeated example that implies infinity concept would never help in creating the real existence of a solution to unsolvable Diaophnintin equations
Consider the simple Diophantine insolvable equation (n^p = 2m^p),
where (p > 2) is a prime number, (n, m, k) are positive integers, where no solution exists in the whole set of positive integers, but what magicians mathematicians usually do plough, by finding large integers for (n, m) for the actually different Diophantine equation of this form: (n^p = 2m^p + k), where (k) is relatively negligible integer in comparison with large (n, m)
And give you always and forever a long RATIONAL solution (in decimal form), since there is no other way
Or the divide the original unsolvable equation as (n/m)^p = x^p = 2), hence the solution (x = n/m = 2^{1/p}), but the shame is so obvious even to any clever school student that is only an approximations that they MUST confess so openly and so loudly,
Also, remember that 2^{1/p), for odd prime (p) is not constructible number, but again can be calculated or CONSTRUCTED as an APPROXIMATION ONLY
The theme is that infinity can't produce any new theorems but fictions only, especially that is only understood by its own so funny definition being unreal number but greater than any number (so funny indeed)
There are many more clearer proofs than this fast one in my posts for sure
BKK
Nobody said approximation is even wrong, but the wrong with those STUBBORN approximators who must confess openly and so loudly that their solutions are APPROXIMATIONS, at least to avoid obvious cheating of people

So this is only the point, but that doesn't mean in any case that there aren't exact results in mathematics, for instance, the Pythagorean theorem is an exact theorem, but [(e) or (Pi) OR p^{1/q}] are not exact numbers,(here (p) is prime, (q) is odd prime)

But, 30^{1/128} is an exact number, where here, exact implies real existence, but not exact implies absolutely non-existence (even though we might need that approximations for our own little needs, which is completely irrelevant issue to the absolute facts of mathematics

And you who ought to think so carfully about the absolute existence of (Pi)! wonder!

So, what was the original definition of an illusion in mind? wonder again!

The true illusion is that you feel keeping coming close enough from an object in mind, where you feel it is almost in your hands, but always and forever in your mind, and out of your hands for sure

So, be satisfied with that always constructible number in your hand, instead of insisting of naming it as transcendental number in your mind, since the later is not there anywhere in reality for sure

BKK
Markus Klyver
2017-07-10 14:21:49 UTC
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Post by b***@gmail.com
How can an approximation be wrong, think about it?
Why should an approximation be a fiction?
3 + 10/71 < pi < 3 + 10/70
is neither wrong nor fiction. To compute with approximation
use some interval arthmetic, you will see
whether you need a better approximation.
Post by bassam king karzeddin
Post by Markus Klyver
That's actually against the definition of what an integer is. But sure, you can declare the existence of multiple infinities if you like.
I remember that I wrote about this issue at Quora, where If we have to accept this infinity concept, then and without loss of generality the air thematic rules must be changed, where this is also would not solve any big puzzle
New rules (say only in positive sense since this can be easily extended to negative sense, where then you fall into infinite number of distinct infinities, where then there isn't any larger infinity, that would immediately invalidate its current existing concept
To explain it in integers first, and in any chosen integer base number system, then there are the known infinities with an endlessly repeated model such as (142857142857142857.....), and there are the unknown random digits infinities such as (2564897364....), or digits of (Pi), or (e), or sqrt(2)
Where then, every unique representation of endless sequence of digits must represent distinct unique infinity
But this is not at all helpful in finding exact solutions, but APPROXIMATION as we do know and practice
[6/7 = 6*10^n/7*10^n] =/= [(6*10^n - 1)/7*10) = 0.857142857142...], when (n) is becoming with infinite sequence of integer digits, sure
Thus (1/7 =/= 0.857142857142...), since the first is well defined but the endless representation is a symptom of a number that tries always and hopelessly to replace or equate the original fraction, but always and forever unsuccessfully, thus not any real number for sure
And since numbers are unique in digital representation, prime factorization and also Geometric reprsentations
You may imagine it as a ghost number that is very good for comparison
Another solid many time repeated example that implies infinity concept would never help in creating the real existence of a solution to unsolvable Diaophnintin equations
Consider the simple Diophantine insolvable equation (n^p = 2m^p),
where (p > 2) is a prime number, (n, m, k) are positive integers, where no solution exists in the whole set of positive integers, but what magicians mathematicians usually do plough, by finding large integers for (n, m) for the actually different Diophantine equation of this form: (n^p = 2m^p + k), where (k) is relatively negligible integer in comparison with large (n, m)
And give you always and forever a long RATIONAL solution (in decimal form), since there is no other way
Or the divide the original unsolvable equation as (n/m)^p = x^p = 2), hence the solution (x = n/m = 2^{1/p}), but the shame is so obvious even to any clever school student that is only an approximations that they MUST confess so openly and so loudly,
Also, remember that 2^{1/p), for odd prime (p) is not constructible number, but again can be calculated or CONSTRUCTED as an APPROXIMATION ONLY
The theme is that infinity can't produce any new theorems but fictions only, especially that is only understood by its own so funny definition being unreal number but greater than any number (so funny indeed)
There are many more clearer proofs than this fast one in my posts for sure
BKK
How can you compare a, in your view a "fiction number", to a very "real and rational number"?
Markus Klyver
2017-07-10 14:19:54 UTC
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Post by bassam king karzeddin
Post by Markus Klyver
That's actually against the definition of what an integer is. But sure, you can declare the existence of multiple infinities if you like.
I remember that I wrote about this issue at Quora, where If we have to accept this infinity concept, then and without loss of generality the air thematic rules must be changed, where this is also would not solve any big puzzle
New rules (say only in positive sense since this can be easily extended to negative sense, where then you fall into infinite number of distinct infinities, where then there isn't any larger infinity, that would immediately invalidate its current existing concept
To explain it in integers first, and in any chosen integer base number system, then there are the known infinities with an endlessly repeated model such as (142857142857142857.....), and there are the unknown random digits infinities such as (2564897364....), or digits of (Pi), or (e), or sqrt(2)
Where then, every unique representation of endless sequence of digits must represent distinct unique infinity
But this is not at all helpful in finding exact solutions, but APPROXIMATION as we do know and practice
[6/7 = 6*10^n/7*10^n] =/= [(6*10^n - 1)/7*10) = 0.857142857142...], when (n) is becoming with infinite sequence of integer digits, sure
Thus (1/7 =/= 0.857142857142...), since the first is well defined but the endless representation is a symptom of a number that tries always and hopelessly to replace or equate the original fraction, but always and forever unsuccessfully, thus not any real number for sure
And since numbers are unique in digital representation, prime factorization and also Geometric reprsentations
You may imagine it as a ghost number that is very good for comparison
Another solid many time repeated example that implies infinity concept would never help in creating the real existence of a solution to unsolvable Diaophnintin equations
Consider the simple Diophantine insolvable equation (n^p = 2m^p),
where (p > 2) is a prime number, (n, m, k) are positive integers, where no solution exists in the whole set of positive integers, but what magicians mathematicians usually do plough, by finding large integers for (n, m) for the actually different Diophantine equation of this form: (n^p = 2m^p + k), where (k) is relatively negligible integer in comparison with large (n, m)
And give you always and forever a long RATIONAL solution (in decimal form), since there is no other way
Or the divide the original unsolvable equation as (n/m)^p = x^p = 2), hence the solution (x = n/m = 2^{1/p}), but the shame is so obvious even to any clever school student that is only an approximations that they MUST confess so openly and so loudly,
Also, remember that 2^{1/p), for odd prime (p) is not constructible number, but again can be calculated or CONSTRUCTED as an APPROXIMATION ONLY
The theme is that infinity can't produce any new theorems but fictions only, especially that is only understood by its own so funny definition being unreal number but greater than any number (so funny indeed)
There are many more clearer proofs than this fast one in my posts for sure
BKK
But there are no infinite integers. As I said, that's against the definition of an integer. So there is no integer with infinite many many digits. All integers are finite. But you can introduce a NEW element and EXTEND the integers. Generally when we do this, then we are going to break things if we are not careful. For example, there's no much sense in ∞ + ∞ = 2∞, so we usually define this new element so that ∞ + ∞ := ∞. Likewise, ∞ * ∞ := ∞, a*∞ = ∞ for any integer a, and so on. ∞ can be a number, but it is not a integer nor a real nor a complex number.

The decimal expansion of 1/7 is very well-defined, but either you're just playing stupid or you don't want to learn anything new. I have REPEATABLY given you the formal definitions and SHOWN how they work. For sure, you are just playing dumb as fuck?

You can repeat your mantra about how the compass-and-straightedge construction is the only valid construction, but that doesn't make it true. You have yet to defend this very narrow-minded view and completely abitary rule.
bassam king karzeddin
2017-07-10 17:26:29 UTC
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Post by Markus Klyver
Post by bassam king karzeddin
Post by Markus Klyver
That's actually against the definition of what an integer is. But sure, you can declare the existence of multiple infinities if you like.
I remember that I wrote about this issue at Quora, where If we have to accept this infinity concept, then and without loss of generality the air thematic rules must be changed, where this is also would not solve any big puzzle
New rules (say only in positive sense since this can be easily extended to negative sense, where then you fall into infinite number of distinct infinities, where then there isn't any larger infinity, that would immediately invalidate its current existing concept
To explain it in integers first, and in any chosen integer base number system, then there are the known infinities with an endlessly repeated model such as (142857142857142857.....), and there are the unknown random digits infinities such as (2564897364....), or digits of (Pi), or (e), or sqrt(2)
Where then, every unique representation of endless sequence of digits must represent distinct unique infinity
But this is not at all helpful in finding exact solutions, but APPROXIMATION as we do know and practice
[6/7 = 6*10^n/7*10^n] =/= [(6*10^n - 1)/7*10) = 0.857142857142...], when (n) is becoming with infinite sequence of integer digits, sure
Thus (1/7 =/= 0.857142857142...), since the first is well defined but the endless representation is a symptom of a number that tries always and hopelessly to replace or equate the original fraction, but always and forever unsuccessfully, thus not any real number for sure
And since numbers are unique in digital representation, prime factorization and also Geometric reprsentations
You may imagine it as a ghost number that is very good for comparison
Another solid many time repeated example that implies infinity concept would never help in creating the real existence of a solution to unsolvable Diaophnintin equations
Consider the simple Diophantine insolvable equation (n^p = 2m^p),
where (p > 2) is a prime number, (n, m, k) are positive integers, where no solution exists in the whole set of positive integers, but what magicians mathematicians usually do plough, by finding large integers for (n, m) for the actually different Diophantine equation of this form: (n^p = 2m^p + k), where (k) is relatively negligible integer in comparison with large (n, m)
And give you always and forever a long RATIONAL solution (in decimal form), since there is no other way
Or the divide the original unsolvable equation as (n/m)^p = x^p = 2), hence the solution (x = n/m = 2^{1/p}), but the shame is so obvious even to any clever school student that is only an approximations that they MUST confess so openly and so loudly,
Also, remember that 2^{1/p), for odd prime (p) is not constructible number, but again can be calculated or CONSTRUCTED as an APPROXIMATION ONLY
The theme is that infinity can't produce any new theorems but fictions only, especially that is only understood by its own so funny definition being unreal number but greater than any number (so funny indeed)
There are many more clearer proofs than this fast one in my posts for sure
BKK
But there are no infinite integers.
Yes, this is my say in many posts, and oddly I assumed its existence to arrive at the contradictions so simply to convence you, but it seems that you get things backwards

As I said, that's against the definition of an integer. So there is no integer with infinite many many digits. All integers are finite.

But in mathematics, you do certainly accept it in all your fabricated decimal expansion for any number and don't tell me that decimal notation is a magical tool that turns those (you call infinite integers to real meaningful number), so remove that point or dot and see your (Pi) clearly, or simply don't ignore its mathematical representation as a ratio of two integers (N/10^m), where (m) is positive integer, and N is integer with
(m + 1) the sequence of digits, and if you insist on seeing it completely, then you must confess that you would require (m) to be with an infinite sequence of digits, so for N, and forget about that (Pi) in your mind

And don't tell me that mathematics can bring it in another form which is not constructible because it is impossible for sure

But you can introduce a NEW element and EXTEND the integers. Generally when we do this, then we are going to break things if we are not careful.

No need really to extend anything to avoid wisely more madness, otherwise we have to break our heads for sure

For example, there's no much sense in ∞ + ∞ = 2∞, so we usually define this new element so that ∞ + ∞ := ∞. Likewise, ∞ * ∞ := ∞, a*∞ = ∞ for any integer a, and so on. ∞ can be a number, but it is not a integer nor a real nor a complex number.

As you said, there is not any sense at all to make many laws and formulas about something really unreal,

And since infinity is not any number, nor anything else, then why do you really associate all your doomed so famous results or theorems with it anymore, maybe for the sweet so easy results or approximations only, never mind, but see that loudly moron that my theorem or results are mainly APPROXIMATIONS, and never EXACT, (The speech is mainly for readers)
Post by Markus Klyver
The decimal expansion of 1/7 is very well-defined, but either you're just playing stupid or you don't want to learn anything new. I have REPEATABLY given you the formal definitions and SHOWN how they work. For sure, you are just playing dumb as fuck?
Still claiming that the decimal expansion of (1/7) is well defined, exactly like so many books, and after so many lessons, wonder!

(1/7) is only (1/7) and nothing else, but its decimal expansion is that ratio of two infinite integers (that you deny openly here), you may call it the ghost of (1/7), it is different as this (10^n - 1)/7*10^n), try it for large integer (n) to understand it, before you make your (n) with infinite sequence of digits, but truly (1/7 = 10^n/7*10^n),

And you would never understand the uniqueness of a number, or see the obvious fallacy trick they brainwashed you for sure

After all, how can I remove all that accumulated dust in your mind that was built over centuries and years in only a few posts
Post by Markus Klyver
You can repeat your mantra about how the compass-and-straightedge construction is the only valid construction, but that doesn't make it true. You have yet to defend this very narrow-minded view and completely arbitrary rule.
As if you could solve any of my published puzzles here for mathematicians, which were about the same issue

And why should I teach you anymore once I know your aimless direction, but at any case, the answer you seek is well written in my posts here only

So, go and search for it if you really interested in learning

And one must not loose temper or becomes so nervous like real idiots to express his own anger or dissatisfactions, there is anther way called general critique that is not any personal, but can convey the theme for sure

BKK
Markus Klyver
2017-07-11 01:23:13 UTC
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Post by bassam king karzeddin
Post by Markus Klyver
Post by bassam king karzeddin
Post by Markus Klyver
That's actually against the definition of what an integer is. But sure, you can declare the existence of multiple infinities if you like.
I remember that I wrote about this issue at Quora, where If we have to accept this infinity concept, then and without loss of generality the air thematic rules must be changed, where this is also would not solve any big puzzle
New rules (say only in positive sense since this can be easily extended to negative sense, where then you fall into infinite number of distinct infinities, where then there isn't any larger infinity, that would immediately invalidate its current existing concept
To explain it in integers first, and in any chosen integer base number system, then there are the known infinities with an endlessly repeated model such as (142857142857142857.....), and there are the unknown random digits infinities such as (2564897364....), or digits of (Pi), or (e), or sqrt(2)
Where then, every unique representation of endless sequence of digits must represent distinct unique infinity
But this is not at all helpful in finding exact solutions, but APPROXIMATION as we do know and practice
[6/7 = 6*10^n/7*10^n] =/= [(6*10^n - 1)/7*10) = 0.857142857142...], when (n) is becoming with infinite sequence of integer digits, sure
Thus (1/7 =/= 0.857142857142...), since the first is well defined but the endless representation is a symptom of a number that tries always and hopelessly to replace or equate the original fraction, but always and forever unsuccessfully, thus not any real number for sure
And since numbers are unique in digital representation, prime factorization and also Geometric reprsentations
You may imagine it as a ghost number that is very good for comparison
Another solid many time repeated example that implies infinity concept would never help in creating the real existence of a solution to unsolvable Diaophnintin equations
Consider the simple Diophantine insolvable equation (n^p = 2m^p),
where (p > 2) is a prime number, (n, m, k) are positive integers, where no solution exists in the whole set of positive integers, but what magicians mathematicians usually do plough, by finding large integers for (n, m) for the actually different Diophantine equation of this form: (n^p = 2m^p + k), where (k) is relatively negligible integer in comparison with large (n, m)
And give you always and forever a long RATIONAL solution (in decimal form), since there is no other way
Or the divide the original unsolvable equation as (n/m)^p = x^p = 2), hence the solution (x = n/m = 2^{1/p}), but the shame is so obvious even to any clever school student that is only an approximations that they MUST confess so openly and so loudly,
Also, remember that 2^{1/p), for odd prime (p) is not constructible number, but again can be calculated or CONSTRUCTED as an APPROXIMATION ONLY
The theme is that infinity can't produce any new theorems but fictions only, especially that is only understood by its own so funny definition being unreal number but greater than any number (so funny indeed)
There are many more clearer proofs than this fast one in my posts for sure
BKK
But there are no infinite integers.
Yes, this is my say in many posts, and oddly I assumed its existence to arrive at the contradictions so simply to convence you, but it seems that you get things backwards
As I said, that's against the definition of an integer. So there is no integer with infinite many many digits. All integers are finite.
But in mathematics, you do certainly accept it in all your fabricated decimal expansion for any number and don't tell me that decimal notation is a magical tool that turns those (you call infinite integers to real meaningful number), so remove that point or dot and see your (Pi) clearly, or simply don't ignore its mathematical representation as a ratio of two integers (N/10^m), where (m) is positive integer, and N is integer with
(m + 1) the sequence of digits, and if you insist on seeing it completely, then you must confess that you would require (m) to be with an infinite sequence of digits, so for N, and forget about that (Pi) in your mind
And don't tell me that mathematics can bring it in another form which is not constructible because it is impossible for sure
But you can introduce a NEW element and EXTEND the integers. Generally when we do this, then we are going to break things if we are not careful.
No need really to extend anything to avoid wisely more madness, otherwise we have to break our heads for sure
For example, there's no much sense in ∞ + ∞ = 2∞, so we usually define this new element so that ∞ + ∞ := ∞. Likewise, ∞ * ∞ := ∞, a*∞ = ∞ for any integer a, and so on. ∞ can be a number, but it is not a integer nor a real nor a complex number.
As you said, there is not any sense at all to make many laws and formulas about something really unreal,
And since infinity is not any number, nor anything else, then why do you really associate all your doomed so famous results or theorems with it anymore, maybe for the sweet so easy results or approximations only, never mind, but see that loudly moron that my theorem or results are mainly APPROXIMATIONS, and never EXACT, (The speech is mainly for readers)
Post by Markus Klyver
The decimal expansion of 1/7 is very well-defined, but either you're just playing stupid or you don't want to learn anything new. I have REPEATABLY given you the formal definitions and SHOWN how they work. For sure, you are just playing dumb as fuck?
Still claiming that the decimal expansion of (1/7) is well defined, exactly like so many books, and after so many lessons, wonder!
(1/7) is only (1/7) and nothing else, but its decimal expansion is that ratio of two infinite integers (that you deny openly here), you may call it the ghost of (1/7), it is different as this (10^n - 1)/7*10^n), try it for large integer (n) to understand it, before you make your (n) with infinite sequence of digits, but truly (1/7 = 10^n/7*10^n),
And you would never understand the uniqueness of a number, or see the obvious fallacy trick they brainwashed you for sure
After all, how can I remove all that accumulated dust in your mind that was built over centuries and years in only a few posts
Post by Markus Klyver
You can repeat your mantra about how the compass-and-straightedge construction is the only valid construction, but that doesn't make it true. You have yet to defend this very narrow-minded view and completely arbitrary rule.
As if you could solve any of my published puzzles here for mathematicians, which were about the same issue
And why should I teach you anymore once I know your aimless direction, but at any case, the answer you seek is well written in my posts here only
So, go and search for it if you really interested in learning
And one must not loose temper or becomes so nervous like real idiots to express his own anger or dissatisfactions, there is anther way called general critique that is not any personal, but can convey the theme for sure
BKK
Sigh. The decimal notation is one way to represent a real number. Consider a function f : N -> {1, 2, 3, 4, 5, 6, 7, 8, 9}. We then DEFINE the notation

f(-n) ... f(-2) f(-1) f(0) . f(1) f(2) f(3) f(4) ...

as the limit of the sum of f(n)/10^n as n -> ∞. For all partial sums, we have that they are bounded, for example every partial sum is bounded by f(0)+1. They are also increasing (though not monotonically as there could be a k such that f(k) = 0). And by the properties of the real numbers we have that EVERY INCREASING SEQUENCE BOUNDED FROM ABOVE HAS A LIMIT IN ℝ. So we know that this series will always have a limit, no matter what f is.

For example, we could consider f such that f(k) = 0 whenever k ≠ 0 and f(k) = 1 for k = 0. We would write this decimal expansion as

1 . 0 0 0 0 0 0 0 0 0 0 ...

And the series f(n)/10^n would indeed have the limit 1.

If you are using the Cauchy construction of real numbers, it's very easy to see that the series will converge in ℝ (simply because ℝ is defined such that all Cauchy sequences in ℝ converges in ℝ). You could also convince yourself about this using the formal limit definition, which I have laid out several times for you. We say that the series, with the partial sums S_n, converges to an element L ∈ ℝ if and only if

For every real ε > 0, there is a N such that whenever n > N, we are guaranteed to have |S_n - L| < ε.

Note that |S_n - L| will always be smaller than 10^(-n+1), so the choice N = (ln(10/x))/(ln(10)) will always work. So the series is guaranteed to converge in ℝ, as proven above.

It has nothing to do with "turning decimals into numbers" or "replacing real numbers with fictitious numbers". Decimal expansions are notation for series I defined and discussed above.

For 1/7 I could define a function f such that

* f(k) = 0, for all k < 1
* f(k) = 1, whenever k = 1 + 6n for some integer n > -1
* f(k) = 4, whenever k = 2 + 6n for some integer n > -1
* f(k) = 2, whenever k = 3 + 6n for some integer n > -1
* f(k) = 8, whenever k = 4 + 6n for some integer n > -1
* f(k) = 5, whenever k = 5 + 6n for some integer n > -1
* f(k) = 7, whenever k = 6 + 6n for some integer n > -1


Now, the sum f(n)/10^n will converge to 1/7 as n -> ∞, so the series have the value 1/7. THUS,

1/7 = 0.142857... Exactly. Per definition.



And also, we don't "make laws" for ∞ when we decide to extend the real numbers. We *define* a new element which satisfy a list of axioms, and we are going to use the symbol "∞" to represent it. We could have equally called it "weeb" or "querk", but the important part is that it has a number of properties it satisfies. One of them being, for every x ∈ R, we have x < weeb. And instead of calling it "weeb", we use the symbol "∞". But there's really not much to it, we define a new element that fall into the orderting and we define operations on this new element. We choose to represent it by "∞", because it has all the properties we would expect an infinite element to have. In this sense, ∞ is a number. But it's not a real number. It's a number in the extended reals.


But you probably don't understand any of this and will keep repeating your mantra: "the compass-and-straightedge construction is the only valid construction". This is something you have made up, and a position you refused to defend. So, you could reject any math that isn't compatible with a such requirement,t but you can't say it's WRONG because of that. EXPLAIN why the compass-and-straightedge construction is the only valid one, or accept that you don't have to have that limitation in your mathematical axiomatic framework.
bassam king karzeddin
2017-07-11 16:53:46 UTC
Permalink
Raw Message
Post by Markus Klyver
Post by bassam king karzeddin
Post by Markus Klyver
Post by bassam king karzeddin
Post by Markus Klyver
That's actually against the definition of what an integer is. But sure, you can declare the existence of multiple infinities if you like.
I remember that I wrote about this issue at Quora, where If we have to accept this infinity concept, then and without loss of generality the air thematic rules must be changed, where this is also would not solve any big puzzle
New rules (say only in positive sense since this can be easily extended to negative sense, where then you fall into infinite number of distinct infinities, where then there isn't any larger infinity, that would immediately invalidate its current existing concept
To explain it in integers first, and in any chosen integer base number system, then there are the known infinities with an endlessly repeated model such as (142857142857142857.....), and there are the unknown random digits infinities such as (2564897364....), or digits of (Pi), or (e), or sqrt(2)
Where then, every unique representation of endless sequence of digits must represent distinct unique infinity
But this is not at all helpful in finding exact solutions, but APPROXIMATION as we do know and practice
[6/7 = 6*10^n/7*10^n] =/= [(6*10^n - 1)/7*10) = 0.857142857142...], when (n) is becoming with infinite sequence of integer digits, sure
Thus (1/7 =/= 0.857142857142...), since the first is well defined but the endless representation is a symptom of a number that tries always and hopelessly to replace or equate the original fraction, but always and forever unsuccessfully, thus not any real number for sure
And since numbers are unique in digital representation, prime factorization and also Geometric reprsentations
You may imagine it as a ghost number that is very good for comparison
Another solid many time repeated example that implies infinity concept would never help in creating the real existence of a solution to unsolvable Diaophnintin equations
Consider the simple Diophantine insolvable equation (n^p = 2m^p),
where (p > 2) is a prime number, (n, m, k) are positive integers, where no solution exists in the whole set of positive integers, but what magicians mathematicians usually do plough, by finding large integers for (n, m) for the actually different Diophantine equation of this form: (n^p = 2m^p + k), where (k) is relatively negligible integer in comparison with large (n, m)
And give you always and forever a long RATIONAL solution (in decimal form), since there is no other way
Or the divide the original unsolvable equation as (n/m)^p = x^p = 2), hence the solution (x = n/m = 2^{1/p}), but the shame is so obvious even to any clever school student that is only an approximations that they MUST confess so openly and so loudly,
Also, remember that 2^{1/p), for odd prime (p) is not constructible number, but again can be calculated or CONSTRUCTED as an APPROXIMATION ONLY
The theme is that infinity can't produce any new theorems but fictions only, especially that is only understood by its own so funny definition being unreal number but greater than any number (so funny indeed)
There are many more clearer proofs than this fast one in my posts for sure
BKK
But there are no infinite integers.
Yes, this is my say in many posts, and oddly I assumed its existence to arrive at the contradictions so simply to convence you, but it seems that you get things backwards
As I said, that's against the definition of an integer. So there is no integer with infinite many many digits. All integers are finite.
But in mathematics, you do certainly accept it in all your fabricated decimal expansion for any number and don't tell me that decimal notation is a magical tool that turns those (you call infinite integers to real meaningful number), so remove that point or dot and see your (Pi) clearly, or simply don't ignore its mathematical representation as a ratio of two integers (N/10^m), where (m) is positive integer, and N is integer with
(m + 1) the sequence of digits, and if you insist on seeing it completely, then you must confess that you would require (m) to be with an infinite sequence of digits, so for N, and forget about that (Pi) in your mind
And don't tell me that mathematics can bring it in another form which is not constructible because it is impossible for sure
But you can introduce a NEW element and EXTEND the integers. Generally when we do this, then we are going to break things if we are not careful.
No need really to extend anything to avoid wisely more madness, otherwise we have to break our heads for sure
For example, there's no much sense in ∞ + ∞ = 2∞, so we usually define this new element so that ∞ + ∞ := ∞. Likewise, ∞ * ∞ := ∞, a*∞ = ∞ for any integer a, and so on. ∞ can be a number, but it is not a integer nor a real nor a complex number.
As you said, there is not any sense at all to make many laws and formulas about something really unreal,
And since infinity is not any number, nor anything else, then why do you really associate all your doomed so famous results or theorems with it anymore, maybe for the sweet so easy results or approximations only, never mind, but see that loudly moron that my theorem or results are mainly APPROXIMATIONS, and never EXACT, (The speech is mainly for readers)
Post by Markus Klyver
The decimal expansion of 1/7 is very well-defined, but either you're just playing stupid or you don't want to learn anything new. I have REPEATABLY given you the formal definitions and SHOWN how they work. For sure, you are just playing dumb as fuck?
Still claiming that the decimal expansion of (1/7) is well defined, exactly like so many books, and after so many lessons, wonder!
(1/7) is only (1/7) and nothing else, but its decimal expansion is that ratio of two infinite integers (that you deny openly here), you may call it the ghost of (1/7), it is different as this (10^n - 1)/7*10^n), try it for large integer (n) to understand it, before you make your (n) with infinite sequence of digits, but truly (1/7 = 10^n/7*10^n),
And you would never understand the uniqueness of a number, or see the obvious fallacy trick they brainwashed you for sure
After all, how can I remove all that accumulated dust in your mind that was built over centuries and years in only a few posts
Post by Markus Klyver
You can repeat your mantra about how the compass-and-straightedge construction is the only valid construction, but that doesn't make it true. You have yet to defend this very narrow-minded view and completely arbitrary rule.
As if you could solve any of my published puzzles here for mathematicians, which were about the same issue
And why should I teach you anymore once I know your aimless direction, but at any case, the answer you seek is well written in my posts here only
So, go and search for it if you really interested in learning
And one must not loose temper or becomes so nervous like real idiots to express his own anger or dissatisfactions, there is anther way called general critique that is not any personal, but can convey the theme for sure
BKK
Sigh. The decimal notation is one way to represent a real number. Consider a function f : N -> {1, 2, 3, 4, 5, 6, 7, 8, 9}. We then DEFINE the notation
f(-n) ... f(-2) f(-1) f(0) . f(1) f(2) f(3) f(4) ...
as the limit of the sum of f(n)/10^n as n -> ∞. For all partial sums, we have that they are bounded, for example every partial sum is bounded by f(0)+1. They are also increasing (though not monotonically as there could be a k such that f(k) = 0). And by the properties of the real numbers we have that EVERY INCREASING SEQUENCE BOUNDED FROM ABOVE HAS A LIMIT IN ℝ. So we know that this series will always have a limit, no matter what f is.
For example, we could consider f such that f(k) = 0 whenever k ≠ 0 and f(k) = 1 for k = 0. We would write this decimal expansion as
1 . 0 0 0 0 0 0 0 0 0 0 ...
And the series f(n)/10^n would indeed have the limit 1.
If you are using the Cauchy construction of real numbers, it's very easy to see that the series will converge in ℝ (simply because ℝ is defined such that all Cauchy sequences in ℝ converges in ℝ). You could also convince yourself about this using the formal limit definition, which I have laid out several times for you. We say that the series, with the partial sums S_n, converges to an element L ∈ ℝ if and only if
For every real ε > 0, there is a N such that whenever n > N, we are guaranteed to have |S_n - L| < ε.
Note that |S_n - L| will always be smaller than 10^(-n+1), so the choice N = (ln(10/x))/(ln(10)) will always work. So the series is guaranteed to converge in ℝ, as proven above.
It has nothing to do with "turning decimals into numbers" or "replacing real numbers with fictitious numbers". Decimal expansions are notation for series I defined and discussed above.
For 1/7 I could define a function f such that
* f(k) = 0, for all k < 1
* f(k) = 1, whenever k = 1 + 6n for some integer n > -1
* f(k) = 4, whenever k = 2 + 6n for some integer n > -1
* f(k) = 2, whenever k = 3 + 6n for some integer n > -1
* f(k) = 8, whenever k = 4 + 6n for some integer n > -1
* f(k) = 5, whenever k = 5 + 6n for some integer n > -1
* f(k) = 7, whenever k = 6 + 6n for some integer n > -1
Now, the sum f(n)/10^n will converge to 1/7 as n -> ∞, so the series have the value 1/7. THUS,
1/7 = 0.142857... Exactly. Per definition.
And also, we don't "make laws" for ∞ when we decide to extend the real numbers. We *define* a new element which satisfy a list of axioms, and we are going to use the symbol "∞" to represent it. We could have equally called it "weeb" or "querk", but the important part is that it has a number of properties it satisfies. One of them being, for every x ∈ R, we have x < weeb. And instead of calling it "weeb", we use the symbol "∞". But there's really not much to it, we define a new element that fall into the orderting and we define operations on this new element. We choose to represent it by "∞", because it has all the properties we would expect an infinite element to have. In this sense, ∞ is a number. But it's not a real number. It's a number in the extended reals.
But you probably don't understand any of this and will keep repeating your mantra: "the compass-and-straightedge construction is the only valid construction". This is something you have made up, and a position you refused to defend. So, you could reject any math that isn't compatible with a such requirement,t but you can't say it's WRONG because of that. EXPLAIN why the compass-and-straightedge construction is the only valid one, or accept that you don't have to have that limitation in your mathematical axiomatic framework.
I understand and appreciate that you repeat what was well established in thousands of mathematics books

But did you ask yourself a very naive question?

Why suddenly in a stage of history of mathematicians had to break numbers to endless pieces to understand them better?

Did the ancient mathematicians were suffering from not understanding the simple fraction (1/7) or any other rational number? wonder!

Doesn't this hint you to something were prepared to get you ready and as a blind obedient for something else that was considered and also proved so unnormal?

And do you really think that divergence of a series is so much different in principle from convergence but in opposite tiny infinitism magnitude?

Or do you think that the Limit of (1/x) = 0, when (x tends to infinity)?

Or do believe in that non-existing infinity?

So, if infinity doesn't belong to R, then how come its inverse belongs to R ? wonder!

Or don't you believe in the uniqueness of a real number?


Then it is so easy to game where you can make any rational number with endless tail of (9), or (d) digits, in any number system

BKK
Markus Klyver
2017-07-11 18:33:39 UTC
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Raw Message
Post by bassam king karzeddin
Post by Markus Klyver
Post by bassam king karzeddin
Post by Markus Klyver
Post by bassam king karzeddin
Post by Markus Klyver
That's actually against the definition of what an integer is. But sure, you can declare the existence of multiple infinities if you like.
I remember that I wrote about this issue at Quora, where If we have to accept this infinity concept, then and without loss of generality the air thematic rules must be changed, where this is also would not solve any big puzzle
New rules (say only in positive sense since this can be easily extended to negative sense, where then you fall into infinite number of distinct infinities, where then there isn't any larger infinity, that would immediately invalidate its current existing concept
To explain it in integers first, and in any chosen integer base number system, then there are the known infinities with an endlessly repeated model such as (142857142857142857.....), and there are the unknown random digits infinities such as (2564897364....), or digits of (Pi), or (e), or sqrt(2)
Where then, every unique representation of endless sequence of digits must represent distinct unique infinity
But this is not at all helpful in finding exact solutions, but APPROXIMATION as we do know and practice
[6/7 = 6*10^n/7*10^n] =/= [(6*10^n - 1)/7*10) = 0.857142857142...], when (n) is becoming with infinite sequence of integer digits, sure
Thus (1/7 =/= 0.857142857142...), since the first is well defined but the endless representation is a symptom of a number that tries always and hopelessly to replace or equate the original fraction, but always and forever unsuccessfully, thus not any real number for sure
And since numbers are unique in digital representation, prime factorization and also Geometric reprsentations
You may imagine it as a ghost number that is very good for comparison
Another solid many time repeated example that implies infinity concept would never help in creating the real existence of a solution to unsolvable Diaophnintin equations
Consider the simple Diophantine insolvable equation (n^p = 2m^p),
where (p > 2) is a prime number, (n, m, k) are positive integers, where no solution exists in the whole set of positive integers, but what magicians mathematicians usually do plough, by finding large integers for (n, m) for the actually different Diophantine equation of this form: (n^p = 2m^p + k), where (k) is relatively negligible integer in comparison with large (n, m)
And give you always and forever a long RATIONAL solution (in decimal form), since there is no other way
Or the divide the original unsolvable equation as (n/m)^p = x^p = 2), hence the solution (x = n/m = 2^{1/p}), but the shame is so obvious even to any clever school student that is only an approximations that they MUST confess so openly and so loudly,
Also, remember that 2^{1/p), for odd prime (p) is not constructible number, but again can be calculated or CONSTRUCTED as an APPROXIMATION ONLY
The theme is that infinity can't produce any new theorems but fictions only, especially that is only understood by its own so funny definition being unreal number but greater than any number (so funny indeed)
There are many more clearer proofs than this fast one in my posts for sure
BKK
But there are no infinite integers.
Yes, this is my say in many posts, and oddly I assumed its existence to arrive at the contradictions so simply to convence you, but it seems that you get things backwards
As I said, that's against the definition of an integer. So there is no integer with infinite many many digits. All integers are finite.
But in mathematics, you do certainly accept it in all your fabricated decimal expansion for any number and don't tell me that decimal notation is a magical tool that turns those (you call infinite integers to real meaningful number), so remove that point or dot and see your (Pi) clearly, or simply don't ignore its mathematical representation as a ratio of two integers (N/10^m), where (m) is positive integer, and N is integer with
(m + 1) the sequence of digits, and if you insist on seeing it completely, then you must confess that you would require (m) to be with an infinite sequence of digits, so for N, and forget about that (Pi) in your mind
And don't tell me that mathematics can bring it in another form which is not constructible because it is impossible for sure
But you can introduce a NEW element and EXTEND the integers. Generally when we do this, then we are going to break things if we are not careful.
No need really to extend anything to avoid wisely more madness, otherwise we have to break our heads for sure
For example, there's no much sense in ∞ + ∞ = 2∞, so we usually define this new element so that ∞ + ∞ := ∞. Likewise, ∞ * ∞ := ∞, a*∞ = ∞ for any integer a, and so on. ∞ can be a number, but it is not a integer nor a real nor a complex number.
As you said, there is not any sense at all to make many laws and formulas about something really unreal,
And since infinity is not any number, nor anything else, then why do you really associate all your doomed so famous results or theorems with it anymore, maybe for the sweet so easy results or approximations only, never mind, but see that loudly moron that my theorem or results are mainly APPROXIMATIONS, and never EXACT, (The speech is mainly for readers)
Post by Markus Klyver
The decimal expansion of 1/7 is very well-defined, but either you're just playing stupid or you don't want to learn anything new. I have REPEATABLY given you the formal definitions and SHOWN how they work. For sure, you are just playing dumb as fuck?
Still claiming that the decimal expansion of (1/7) is well defined, exactly like so many books, and after so many lessons, wonder!
(1/7) is only (1/7) and nothing else, but its decimal expansion is that ratio of two infinite integers (that you deny openly here), you may call it the ghost of (1/7), it is different as this (10^n - 1)/7*10^n), try it for large integer (n) to understand it, before you make your (n) with infinite sequence of digits, but truly (1/7 = 10^n/7*10^n),
And you would never understand the uniqueness of a number, or see the obvious fallacy trick they brainwashed you for sure
After all, how can I remove all that accumulated dust in your mind that was built over centuries and years in only a few posts
Post by Markus Klyver
You can repeat your mantra about how the compass-and-straightedge construction is the only valid construction, but that doesn't make it true. You have yet to defend this very narrow-minded view and completely arbitrary rule.
As if you could solve any of my published puzzles here for mathematicians, which were about the same issue
And why should I teach you anymore once I know your aimless direction, but at any case, the answer you seek is well written in my posts here only
So, go and search for it if you really interested in learning
And one must not loose temper or becomes so nervous like real idiots to express his own anger or dissatisfactions, there is anther way called general critique that is not any personal, but can convey the theme for sure
BKK
Sigh. The decimal notation is one way to represent a real number. Consider a function f : N -> {1, 2, 3, 4, 5, 6, 7, 8, 9}. We then DEFINE the notation
f(-n) ... f(-2) f(-1) f(0) . f(1) f(2) f(3) f(4) ...
as the limit of the sum of f(n)/10^n as n -> ∞. For all partial sums, we have that they are bounded, for example every partial sum is bounded by f(0)+1. They are also increasing (though not monotonically as there could be a k such that f(k) = 0). And by the properties of the real numbers we have that EVERY INCREASING SEQUENCE BOUNDED FROM ABOVE HAS A LIMIT IN ℝ. So we know that this series will always have a limit, no matter what f is.
For example, we could consider f such that f(k) = 0 whenever k ≠ 0 and f(k) = 1 for k = 0. We would write this decimal expansion as
1 . 0 0 0 0 0 0 0 0 0 0 ...
And the series f(n)/10^n would indeed have the limit 1.
If you are using the Cauchy construction of real numbers, it's very easy to see that the series will converge in ℝ (simply because ℝ is defined such that all Cauchy sequences in ℝ converges in ℝ). You could also convince yourself about this using the formal limit definition, which I have laid out several times for you. We say that the series, with the partial sums S_n, converges to an element L ∈ ℝ if and only if
For every real ε > 0, there is a N such that whenever n > N, we are guaranteed to have |S_n - L| < ε.
Note that |S_n - L| will always be smaller than 10^(-n+1), so the choice N = (ln(10/x))/(ln(10)) will always work. So the series is guaranteed to converge in ℝ, as proven above.
It has nothing to do with "turning decimals into numbers" or "replacing real numbers with fictitious numbers". Decimal expansions are notation for series I defined and discussed above.
For 1/7 I could define a function f such that
* f(k) = 0, for all k < 1
* f(k) = 1, whenever k = 1 + 6n for some integer n > -1
* f(k) = 4, whenever k = 2 + 6n for some integer n > -1
* f(k) = 2, whenever k = 3 + 6n for some integer n > -1
* f(k) = 8, whenever k = 4 + 6n for some integer n > -1
* f(k) = 5, whenever k = 5 + 6n for some integer n > -1
* f(k) = 7, whenever k = 6 + 6n for some integer n > -1
Now, the sum f(n)/10^n will converge to 1/7 as n -> ∞, so the series have the value 1/7. THUS,
1/7 = 0.142857... Exactly. Per definition.
And also, we don't "make laws" for ∞ when we decide to extend the real numbers. We *define* a new element which satisfy a list of axioms, and we are going to use the symbol "∞" to represent it. We could have equally called it "weeb" or "querk", but the important part is that it has a number of properties it satisfies. One of them being, for every x ∈ R, we have x < weeb. And instead of calling it "weeb", we use the symbol "∞". But there's really not much to it, we define a new element that fall into the orderting and we define operations on this new element. We choose to represent it by "∞", because it has all the properties we would expect an infinite element to have. In this sense, ∞ is a number. But it's not a real number. It's a number in the extended reals.
But you probably don't understand any of this and will keep repeating your mantra: "the compass-and-straightedge construction is the only valid construction". This is something you have made up, and a position you refused to defend. So, you could reject any math that isn't compatible with a such requirement,t but you can't say it's WRONG because of that. EXPLAIN why the compass-and-straightedge construction is the only valid one, or accept that you don't have to have that limitation in your mathematical axiomatic framework.
I understand and appreciate that you repeat what was well established in thousands of mathematics books
But did you ask yourself a very naive question?
Why suddenly in a stage of history of mathematicians had to break numbers to endless pieces to understand them better?
Did the ancient mathematicians were suffering from not understanding the simple fraction (1/7) or any other rational number? wonder!
Doesn't this hint you to something were prepared to get you ready and as a blind obedient for something else that was considered and also proved so unnormal?
And do you really think that divergence of a series is so much different in principle from convergence but in opposite tiny infinitism magnitude?
Or do you think that the Limit of (1/x) = 0, when (x tends to infinity)?
Or do believe in that non-existing infinity?
So, if infinity doesn't belong to R, then how come its inverse belongs to R ? wonder!
Or don't you believe in the uniqueness of a real number?
Then it is so easy to game where you can make any rational number with endless tail of (9), or (d) digits, in any number system
BKK
Let me answer your questions. Ancient mathematics was often built around empirical observations and idealized Euclidean geometry. If you had an apple and an other apple, you obviously had two apples. Hence, 1 + 1 = 2.

But as history went on, people started to formalize mathematics. Now: I admit foundation mathematics will not ever be solved, but most mathematicians agree about an axiomatic and set theoretic ground for mathematics. Ancient Greeks saw mathematics as "pure geometry" (Euclidean geometry, I must add) but this view was for mathematical and philosophical reasons unsatisfactory. In fact, Pythagoras needed measure theory *to even state his teorems*. Now we have this primitive notation about a "set" and build our mathematics on that.

So, with that in mind, remember the formal definition of rationals as equivalence classes of tuples of integers. The Ancient understanding of 1/7 was "you have something, a unit, and cut it in seven equal parts". The modern definition of 1/7 is the equivalence class [(1,7)] where (a, b) ~ (c, d) if and only if ad - bc = 0.

Ancient mathematics lacked rigorousness and often relied on vague primitive notions. That don't mean it wasn't mathematics. It was just not very formal or axiomatically unsatisfactory.

Divergence is the opposite of convergence. A series that does not converge is called a divergent series. I don't understand what you mean by "unnormal". Divergent series differ from convergent series in the sense that divergent series don't converge.

Yes, the limit of 1/x as x --> ∞ is 0. Consider the formal definition again:

∀ε>0 ∃N : x>N --> |1/x - L|<ε

Now, with the limit L = 0, we have the last inequality as |1/x| = 1/|x|<ε.

We see that a good choice is N = 1/ε, because whenever x>N, we would have

1/|x| < 1/|N| = 1/|1/ε| = ε


So, YES, lim_{x --> ∞} 1/x = 0. Note how this is a LIMIT though. The limit of 1/x as x --> ∞ is not the same as 1/∞. ∞ is not a real number, and so 1/∞ is not meaningful either.

Though in the EXTENDED reals, ∞ *is* a number. Note that 1/∞ is only a number if you extend the operation division to the extended reals as well. If you make the definition a/∞ := 0 for any real number a, then 1/∞ = 0. Here, 1/∞ has meaning (but only because we extended division as well). If you don't extend the reals, it doesn't make much sense to define division by ∞ either.

But 0 isn't the multiplicative inverse inverse of ∞. If that were the case, then 0*∞ = ∞*0 = 1. But multiplication by ∞ is left undefined. This is actually a good observation, because it demonstrates the extended reals fails the field axioms. So the extended reals is not a field. And since lacks a multiplicative inverse, it's not even a group. In fact, extended reals is not even a semigroup. I hope this clears things up.

A real number is unique, since equivalence classes and sets are unique. I mean, only one set B satisfies B = A, namely A itself.

Lastly, I would like to hear why you think the compass-and-straightedge construction is the only valid construction.
Me
2017-07-11 20:52:01 UTC
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Post by bassam king karzeddin
Why suddenly in a stage of history of mathematicians had to break numbers to
endless pieces to understand them better?
It's called (scientific) progress.

You know, there's something like development in most sciences.
bassam king karzeddin
2017-06-22 06:24:39 UTC
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Post by bassam king karzeddin
Maybe the question is long enough to appear in the question title, so here it is again
Why does Infinity concept represent the hen that bleaches daily gold eggs for professional mathematicians?
Also, infinity was proven as a junk concept and mainly from its basic definition being unreal in terms of numbers and also being greater than any number, where this type of a definition sounds so crazy and a kind of hallucination really? wonder!
However, the existence which matters a lot in this whole story, where reality basically means existence
So, assuming for a while that concept of infinity is a nonsense concept, then many established facts, theorems, formulas, ... etc in mathematics would immediately be naked and unprotected where it collapses to doubtful untrue and absolutely wrong results for sure
So, what are the immediate subsequences that you might be able to logically conclude if you once drop this doubtful concept say for a while?
Regards
Bassam King Karzeddin
May 23, 2017
And the fakery alleged Top Professional mathematicians say loudly and so shamelessly that Infinity isn't a real number, nor any number, but oddly larger than any number, wonder!

And naturally, the very poor minds follow, of course for their own needed reasons for sure

So, Infinity is much longer than any tree, and heavier than any galaxy, and faster than any speed,.., etc!

What is a nonsense mathematics this really?

Can not anyone invent something really meaningful? wonder!

But please avoid falling in more nonsense concepts as INFINITIES.

BKK
Markus Klyver
2017-07-09 15:11:44 UTC
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Post by bassam king karzeddin
Post by bassam king karzeddin
Maybe the question is long enough to appear in the question title, so here it is again
Why does Infinity concept represent the hen that bleaches daily gold eggs for professional mathematicians?
Also, infinity was proven as a junk concept and mainly from its basic definition being unreal in terms of numbers and also being greater than any number, where this type of a definition sounds so crazy and a kind of hallucination really? wonder!
However, the existence which matters a lot in this whole story, where reality basically means existence
So, assuming for a while that concept of infinity is a nonsense concept, then many established facts, theorems, formulas, ... etc in mathematics would immediately be naked and unprotected where it collapses to doubtful untrue and absolutely wrong results for sure
So, what are the immediate subsequences that you might be able to logically conclude if you once drop this doubtful concept say for a while?
Regards
Bassam King Karzeddin
May 23, 2017
And the fakery alleged Top Professional mathematicians say loudly and so shamelessly that Infinity isn't a real number, nor any number, but oddly larger than any number, wonder!
And naturally, the very poor minds follow, of course for their own needed reasons for sure
So, Infinity is much longer than any tree, and heavier than any galaxy, and faster than any speed,.., etc!
What is a nonsense mathematics this really?
Can not anyone invent something really meaningful? wonder!
But please avoid falling in more nonsense concepts as INFINITIES.
BKK
" And the fakery alleged Top Professional mathematicians say loudly and so shamelessly that Infinity isn't a real number, nor any number, but oddly larger than any number, wonder! "

Infinity is not a real number, but you can EXTEND the real numbers to include an "infinite element". You don't seem to grasp this very simple concept any math and physics undergraduate does.
Me
2017-07-09 17:05:35 UTC
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Post by Markus Klyver
Infinity is not a real number, but you can EXTEND the real numbers to include
an "infinite element". You don't seem to grasp this very simple concept any
math and physics undergraduate does.
See: https://en.wikipedia.org/wiki/Extended_real_number_line
bassam king karzeddin
2017-07-09 17:25:53 UTC
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Post by Me
Post by Markus Klyver
Infinity is not a real number, but you can EXTEND the real numbers to include
an "infinite element". You don't seem to grasp this very simple concept any
math and physics undergraduate does.
See: https://en.wikipedia.org/wiki/Extended_real_number_line
But the whole problem that infinity is not existing as a constructible number, in words how can I extend my reals to something intangible, (i.e only in your or generally human mind, and I guess you had been learnt what generally a human mind could really contain), especially the modern professional human minds, that are full of fairy fiction stories for sure

By the way, did you see that LITTLE FINITE INTEGER I already gave you, or do you think that is infinite integer

Or can you deny that is not a FINITE INTEGER

And still, the lesson wouldn't work with you most likely, but hey, it doesn't any matter for sure

BKK
Me
2017-07-09 21:33:02 UTC
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the modern professional human minds [...] are full of [...] fiction stories
for sure
Yeah, they are called mathematical theories.

See:
https://plato.stanford.edu/entries/fictionalism-mathematics/
https://plato.stanford.edu/entries/fictionalism/
http://www.iep.utm.edu/mathfict/
bassam king karzeddin
2017-07-10 09:48:28 UTC
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Post by Me
the modern professional human minds [...] are full of [...] fiction stories
for sure
Yeah, they are called mathematical theories.
https://plato.stanford.edu/entries/fictionalism-mathematics/
https://plato.stanford.edu/entries/fictionalism/
http://www.iep.utm.edu/mathfict/
Nice articles, but I don't think that a common typo mathematicians would be able to digest anything out of that since they generally behave like machine calculators and according to the installed program with themselves so strictly

Thanks
BBK
Me
2017-07-10 12:17:49 UTC
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mathematicians [...] generally behave like machine calculators and according
to the installed program with themselves so strictly
Actually, I'd consider this to be a rather good thing, after all it ensures for *correct* results. (Hint: You don't use and rely on the results of pocket calculators?)
Markus Klyver
2017-07-10 02:46:34 UTC
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Post by bassam king karzeddin
Post by Me
Post by Markus Klyver
Infinity is not a real number, but you can EXTEND the real numbers to include
an "infinite element". You don't seem to grasp this very simple concept any
math and physics undergraduate does.
See: https://en.wikipedia.org/wiki/Extended_real_number_line
But the whole problem that infinity is not existing as a constructible number, in words how can I extend my reals to something intangible, (i.e only in your or generally human mind, and I guess you had been learnt what generally a human mind could really contain), especially the modern professional human minds, that are full of fairy fiction stories for sure
By the way, did you see that LITTLE FINITE INTEGER I already gave you, or do you think that is infinite integer
Or can you deny that is not a FINITE INTEGER
And still, the lesson wouldn't work with you most likely, but hey, it doesn't any matter for sure
BKK
And why should the compass-and-straightedge construction be he only valid way tot generate/construct new mathematical objects? You have yet to explain this! It's a pretty narrow-minded view and a completely abitary rule.
bassam king karzeddin
2017-07-15 13:28:32 UTC
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Post by bassam king karzeddin
Maybe the question is long enough to appear in the question title, so here it is again
Why does Infinity concept represent the hen that bleaches daily gold eggs for professional mathematicians?
Also, infinity was proven as a junk concept and mainly from its basic definition being unreal in terms of numbers and also being greater than any number, where this type of a definition sounds so crazy and a kind of hallucination really? wonder!
However, the existence which matters a lot in this whole story, where reality basically means existence
So, assuming for a while that concept of infinity is a nonsense concept, then many established facts, theorems, formulas, ... etc in mathematics would immediately be naked and unprotected where it collapses to doubtful untrue and absolutely wrong results for sure
So, what are the immediate subsequences that you might be able to logically conclude if you once drop this doubtful concept say for a while?
Regards
Bassam King Karzeddin
May 23, 2017
So, did you understand what was that hen that bleaches gold for the top professional mathematicians, especially those who moderate at Wikipedia or Top Journals or top UNIVERSITIES? Wonder!

And do you think that they would stop egging much more?
Only you can stop those fake gold eggs for sure unless of course, you are so pregnant with many eggs that you want to lay down. no wonder here!

So, go to your endless Paradise and bring back many golden eggs for sure

Since there, there are still uncountable number of eggs that can fill the galaxy not so far away from now, sure

BKK
Markus Klyver
2017-07-15 15:18:53 UTC
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Post by bassam king karzeddin
Post by bassam king karzeddin
Maybe the question is long enough to appear in the question title, so here it is again
Why does Infinity concept represent the hen that bleaches daily gold eggs for professional mathematicians?
Also, infinity was proven as a junk concept and mainly from its basic definition being unreal in terms of numbers and also being greater than any number, where this type of a definition sounds so crazy and a kind of hallucination really? wonder!
However, the existence which matters a lot in this whole story, where reality basically means existence
So, assuming for a while that concept of infinity is a nonsense concept, then many established facts, theorems, formulas, ... etc in mathematics would immediately be naked and unprotected where it collapses to doubtful untrue and absolutely wrong results for sure
So, what are the immediate subsequences that you might be able to logically conclude if you once drop this doubtful concept say for a while?
Regards
Bassam King Karzeddin
May 23, 2017
So, did you understand what was that hen that bleaches gold for the top professional mathematicians, especially those who moderate at Wikipedia or Top Journals or top UNIVERSITIES? Wonder!
And do you think that they would stop egging much more?
Only you can stop those fake gold eggs for sure unless of course, you are so pregnant with many eggs that you want to lay down. no wonder here!
So, go to your endless Paradise and bring back many golden eggs for sure
Since there, there are still uncountable number of eggs that can fill the galaxy not so far away from now, sure
BKK
Did you bother to read my post? I have explained these things for you, over and over.
z***@outlook.com
2017-07-16 08:22:16 UTC
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Infinity is useful and it is rigorously defined in mathematics, it is not an issue.
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