Discussion:
Prime Staircase Conjecture;; the reverse of Goldbach Conjecture, and its pretty implication of some pattern to primes
Archimedes Plutonium
2017-08-10 09:45:20 UTC
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Now, I do not recall when I started with the Staircase conjecture, a conjecture original to me-- was it 5 years ago, that I started this? Do not recall but can go back and find out in the post date time headings.

Anyway, what the Staircase Conjecture is, it is the reverse of Goldbach in that Goldbach wants to decompose even numbers into prime addition. Staircase wants to build even numbers starting with a toolbox of primes and adding onto existing primes. Once you see the shemata below, you instantly recognize what is going on::

Caution: I am using 1 as Unit Prime

1+1 = 2
1+3 = 4
1+5 = 6
3+5 = 8
5+5 = 10
7+5 = 12
1+13 = 14
3+ 13 = 16
5 + 13 = 18
7 + 13 = 20
3 + 19 = 22

Now let me stop there and point out a iteration, that I strive to start each iteration with 1 so I can use the 1,3,5,7 pattern, so I want that pattern to appear as often as possible, and it was temporarily broken with 22. but starts right back up again at 24

1 + 23 = 24
3+ 23 = 26
5 + 23 = 28
7 + 23 = 30

Now, let me stop there and state the Conjecture I have in mind, in full.

STAIRCASE CONJECTURE:: Given a bag of primes as tools, generate all Even Numbers in as best of a pattern as possible, using 1 in that bag, and, I conjecture that in the Grid Systems of Mathematics that each prior Grid has sufficient primes as the toolkit to generate all the Even numbers up to the next higher Grid.

So, what do I mean? I mean in the example started above for which I will post all the even up to 100, that the primes in the 10 Grid which are 1, 2, 3, 5, 7, and omitting 2, that those primes suffice to build all the evens from 0 to 100. Now, the conjecture implies that all the primes in 0 to 100 (omit 2) suffice to build all the evens from 0 to 1000, and so on so forth in higher Grids.

What this means is that the Prime gaps are never so large that previous Grid primes can span that gap.

In 10 Grid the largest gap was 8,9,10. In 100 Grid, the largest prime gap was from 89 to 97 for a gap of 8 and it tested the conjecture with 7+89 = 96. So if the number 89 were not prime but instead no primes from 83 to 97, then the Staircase Conjecture would be instantly wrong.

Now I have to review the largest prime gap span in 1000 Grid, but I am confident that the primes in 100 Grid easily span the gap.

Now, there are many interesting questions about the maximum order we can assign the building. We would want as many as possible of runs of 1, 3, 5, 7 for that gives us immediately four even numbers in a row. And we ask the question, is the number of those runs involve pi or 2.71... So looking at my data sheet, I count up 7.5 runs of 1,3,5,7 and I count 5 runs of 3,5,7. So that would be 30 of the 50 even numbers are of the largest run.

So now, I need data from the 1000 Grid, to see if pi or 2.71... is involved.

And, perhaps we can spot a pattern in primes.

But a cool interesting feature of the Staircase Conjecture, is that if true, it instantly proves Goldbach, for it is the reverse of Goldbach.

AP
b***@gmail.com
2017-08-10 10:15:05 UTC
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You got yourself a new nonsense hobby?
New chapter in your book of mongo math?
Post by Archimedes Plutonium
Now, I do not recall when I started with the Staircase conjecture, a conjecture original to me-- was it 5 years ago, that I started this? Do not recall but can go back and find out in the post date time headings.
Caution: I am using 1 as Unit Prime
1+1 = 2
1+3 = 4
1+5 = 6
3+5 = 8
5+5 = 10
7+5 = 12
1+13 = 14
3+ 13 = 16
5 + 13 = 18
7 + 13 = 20
3 + 19 = 22
Now let me stop there and point out a iteration, that I strive to start each iteration with 1 so I can use the 1,3,5,7 pattern, so I want that pattern to appear as often as possible, and it was temporarily broken with 22. but starts right back up again at 24
1 + 23 = 24
3+ 23 = 26
5 + 23 = 28
7 + 23 = 30
Now, let me stop there and state the Conjecture I have in mind, in full.
STAIRCASE CONJECTURE:: Given a bag of primes as tools, generate all Even Numbers in as best of a pattern as possible, using 1 in that bag, and, I conjecture that in the Grid Systems of Mathematics that each prior Grid has sufficient primes as the toolkit to generate all the Even numbers up to the next higher Grid.
So, what do I mean? I mean in the example started above for which I will post all the even up to 100, that the primes in the 10 Grid which are 1, 2, 3, 5, 7, and omitting 2, that those primes suffice to build all the evens from 0 to 100. Now, the conjecture implies that all the primes in 0 to 100 (omit 2) suffice to build all the evens from 0 to 1000, and so on so forth in higher Grids.
What this means is that the Prime gaps are never so large that previous Grid primes can span that gap.
In 10 Grid the largest gap was 8,9,10. In 100 Grid, the largest prime gap was from 89 to 97 for a gap of 8 and it tested the conjecture with 7+89 = 96. So if the number 89 were not prime but instead no primes from 83 to 97, then the Staircase Conjecture would be instantly wrong.
Now I have to review the largest prime gap span in 1000 Grid, but I am confident that the primes in 100 Grid easily span the gap.
Now, there are many interesting questions about the maximum order we can assign the building. We would want as many as possible of runs of 1, 3, 5, 7 for that gives us immediately four even numbers in a row. And we ask the question, is the number of those runs involve pi or 2.71... So looking at my data sheet, I count up 7.5 runs of 1,3,5,7 and I count 5 runs of 3,5,7. So that would be 30 of the 50 even numbers are of the largest run.
So now, I need data from the 1000 Grid, to see if pi or 2.71... is involved.
And, perhaps we can spot a pattern in primes.
But a cool interesting feature of the Staircase Conjecture, is that if true, it instantly proves Goldbach, for it is the reverse of Goldbach.
AP
Archimedes Plutonium
2017-08-10 10:25:27 UTC
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Finishing the table out to 100, using 1 as unit prime

1+1 = 2
1+3 = 4
1+5 = 6
3+5 = 8
5+5 = 10
7+5 = 12
1+13 = 14
3+ 13 = 16
5 + 13 = 18
7 + 13 = 20
3 + 19 = 22

1 + 23 = 24
3+ 23 = 26
5 + 23 = 28
7 + 23 = 30
1 + 31 = 32
3 + 31 = 34
5 + 31 = 36
7 + 31 = 38
3 + 37 = 40
1 + 41 = 42
3+ 41 = 44
5 + 41 = 46
7 + 41 = 48
3 + 47 = 50
5 + 47 = 52
7 + 47 = 54
3 + 53 = 56
5 + 53 = 58
7 + 53 = 60
3 + 59 = 62
5 + 59 = 64
7 + 59 = 66
1 + 67 = 68
3 + 67 = 70
5 + 67 = 72
7 + 67 = 74
3+ 73 = 76
5 + 73 = 78
7 + 73 = 80
3 + 79 = 82
1 + 83 = 84
3+ 83 = 86
5 + 83 = 88
7 + 83 = 90
3 + 89 = 92
5 + 89 = 94
7 + 89 = 96
1 +97 = 98
3 + 97 = 100

Now, note, if I did not use 1 as Prime Unit, then I would have had a horrible time of coming up with 98 for I would have had to find 13 + 83 and the 13 would have broken the conjecture because the conjecture says all primes in prior Grid can be used, none beyond. So to build all even in 0 to 100 I could only use 1,3,5,7 and they do the job nicely.

So, the amazing thing about the Staircase Conjecture, is that a proof of it, instantly proves Goldbach.

So the proof of Goldbach was really fast simple and easy with the Axiom of Uniqueness. But is a proof of Staircase also fast and easy?

Well, unlike Goldbach, the Staircase has far more ORDER to it, far more structure and order and a semipattern, whereas Goldbach is hit and miss in Matrix Columns.

So, a proof of Staircase is going to be more involved than Goldbach due to the semi pattern.

What would a Staircase proof look like? Well, it is obvious that it hinges on the Largest Prime Gap within any particular Grid. For if that Prime Gap is larger than the largest prime in the prior previous Grid, then instantly the Staircase has a counterexample.

I forgot the largest prime gap in 0 to 1000. If it is larger than 97, then we are in serious trouble with Staircase.

And is Staircase is true, then we have a important side conjecture-- the number relationship of the prime gap in a Grid versus the largest prime in the prior Grid.

So for example the largest prime gap in 100 Grid is from 89 to 97 and the largest prime in 10 Grid is 7, so I needed exactly 7 to span the largest prime gap. I suspect in 1000 Grid, no prime gap is anywhere near that of 97 length. And so if Staircase is true, begs the question of that relationship of prime gap and largest prime.

AP
b***@gmail.com
2017-08-10 11:12:34 UTC
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AP brain farto, as usual posting complete nonsense,
this already for 30 years, not a single line of math.
Post by Archimedes Plutonium
Finishing the table out to 100, using 1 as unit prime
1+1 = 2
1+3 = 4
1+5 = 6
3+5 = 8
5+5 = 10
7+5 = 12
1+13 = 14
3+ 13 = 16
5 + 13 = 18
7 + 13 = 20
3 + 19 = 22
1 + 23 = 24
3+ 23 = 26
5 + 23 = 28
7 + 23 = 30
1 + 31 = 32
3 + 31 = 34
5 + 31 = 36
7 + 31 = 38
3 + 37 = 40
1 + 41 = 42
3+ 41 = 44
5 + 41 = 46
7 + 41 = 48
3 + 47 = 50
5 + 47 = 52
7 + 47 = 54
3 + 53 = 56
5 + 53 = 58
7 + 53 = 60
3 + 59 = 62
5 + 59 = 64
7 + 59 = 66
1 + 67 = 68
3 + 67 = 70
5 + 67 = 72
7 + 67 = 74
3+ 73 = 76
5 + 73 = 78
7 + 73 = 80
3 + 79 = 82
1 + 83 = 84
3+ 83 = 86
5 + 83 = 88
7 + 83 = 90
3 + 89 = 92
5 + 89 = 94
7 + 89 = 96
1 +97 = 98
3 + 97 = 100
Now, note, if I did not use 1 as Prime Unit, then I would have had a horrible time of coming up with 98 for I would have had to find 13 + 83 and the 13 would have broken the conjecture because the conjecture says all primes in prior Grid can be used, none beyond. So to build all even in 0 to 100 I could only use 1,3,5,7 and they do the job nicely.
So, the amazing thing about the Staircase Conjecture, is that a proof of it, instantly proves Goldbach.
So the proof of Goldbach was really fast simple and easy with the Axiom of Uniqueness. But is a proof of Staircase also fast and easy?
Well, unlike Goldbach, the Staircase has far more ORDER to it, far more structure and order and a semipattern, whereas Goldbach is hit and miss in Matrix Columns.
So, a proof of Staircase is going to be more involved than Goldbach due to the semi pattern.
What would a Staircase proof look like? Well, it is obvious that it hinges on the Largest Prime Gap within any particular Grid. For if that Prime Gap is larger than the largest prime in the prior previous Grid, then instantly the Staircase has a counterexample.
I forgot the largest prime gap in 0 to 1000. If it is larger than 97, then we are in serious trouble with Staircase.
And is Staircase is true, then we have a important side conjecture-- the number relationship of the prime gap in a Grid versus the largest prime in the prior Grid.
So for example the largest prime gap in 100 Grid is from 89 to 97 and the largest prime in 10 Grid is 7, so I needed exactly 7 to span the largest prime gap. I suspect in 1000 Grid, no prime gap is anywhere near that of 97 length. And so if Staircase is true, begs the question of that relationship of prime gap and largest prime.
AP
Archimedes Plutonium
2017-08-10 12:13:12 UTC
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Alright, reviewed the last time I worked on Staircase and is the span of 887 to 907, span of 20 as largest gap from 0 to 1000

884 = 883+1
886 = 883 +3
888 = 883+5
890 = 883 +7
892 = 887 + 5
894 = 887 + 7
896 = 883 + 13
898 = 881 + 17
900 = 881 + 19
902 = 883 + 19
904 = 881 + 23
906 = 877 + 29

So the largest gap from 887 to 907 requires 29 to mend a bridge, and nowhere near taking up all the other primes from 1 to 97 to build the Evens from 0 to 1000.

Now quite sure why I demanded a prior Grid primes was the maximum allowed primes.

Only in the case of 10 Grid to 100 Grid, are all primes (other than 2) were used. In the 1000 Grid, only the primes up to and including 29 were used or needed. So only 40% of the primes that I could use, were actually used.

Thinking about a proof of Staircase, and it comes back to the same proof method of Goldbach. We have to examine the Matrix Columns of all the Evens. Realize that each Column has a Bertrand prime on leftside and one on rightside. The Bertrand Primes have to line up, because of Axiom of Uniqueness, and, perhaps I need an axiom of Complimentarity, simply says add is the compliment of multiply and vice versa.

Define Complimentarity as a property in which two things are complimentary if they are different, yet, they are always joined, always necessary to have the two together. Together, but different.

I see no way to prove that some far away Even Number has a prime nearby and has just the right distance prime in the toolbox that reaches the Even Number. I see no way of proving that, unless you say that the Even Number has a Matrix Column and has two Bertrand Primes, and they must line up for then , those two Bertrand Primes when multiplied to form a Two Prime Composite, that number does not exist, yet it does exist.

So, here I see that there can be no different proof method for Staircase, but rather, the same method used on Goldbach.

This indicates, the assertion that Goldbach and Staircase are equivalent propositions, yet from all viewpoints, the Staircase looks so much more orderly and patterned while Goldbach is more shrouded.

AP
b***@gmail.com
2017-08-10 14:52:48 UTC
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You mean Goldbach is the oval and the Staircase
is the circle? Not very data analyst like,

normally you try to express such data properties
by some numbers that you can compute from the data.
Post by Archimedes Plutonium
This indicates, the assertion that Goldbach and Staircase are equivalent propositions, yet from all viewpoints, the Staircase looks so much more orderly and patterned while Goldbach is more shrouded.
AP
Archimedes Plutonium
2017-08-11 00:47:23 UTC
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Post by Archimedes Plutonium
Alright, reviewed the last time I worked on Staircase and is the span of 887 to 907, span of 20 as largest gap from 0 to 1000
884 = 883+1
886 = 883 +3
888 = 883+5
890 = 883 +7
892 = 887 + 5
894 = 887 + 7
896 = 883 + 13
898 = 881 + 17
900 = 881 + 19
902 = 883 + 19
904 = 881 + 23
906 = 877 + 29
So the largest gap from 887 to 907 requires 29 to mend a bridge, and nowhere near taking up all the other primes from 1 to 97 to build the Evens from 0 to 1000.
Now quite sure why I demanded a prior Grid primes was the maximum allowed primes.
Only in the case of 10 Grid to 100 Grid, are all primes (other than 2) were used. In the 1000 Grid, only the primes up to and including 29 were used or needed. So only 40% of the primes that I could use, were actually used.
Thinking about a proof of Staircase, and it comes back to the same proof method of Goldbach. We have to examine the Matrix Columns of all the Evens. Realize that each Column has a Bertrand prime on leftside and one on rightside. The Bertrand Primes have to line up, because of Axiom of Uniqueness, and, perhaps I need an axiom of Complimentarity, simply says add is the compliment of multiply and vice versa.
Define Complimentarity as a property in which two things are complimentary if they are different, yet, they are always joined, always necessary to have the two together. Together, but different.
I see no way to prove that some far away Even Number has a prime nearby and has just the right distance prime in the toolbox that reaches the Even Number. I see no way of proving that, unless you say that the Even Number has a Matrix Column and has two Bertrand Primes, and they must line up for then , those two Bertrand Primes when multiplied to form a Two Prime Composite, that number does not exist, yet it does exist.
So, here I see that there can be no different proof method for Staircase, but rather, the same method used on Goldbach.
This indicates, the assertion that Goldbach and Staircase are equivalent propositions, yet from all viewpoints, the Staircase looks so much more orderly and patterned while Goldbach is more shrouded.
AP
Alright, I need to stop here and sort things out.

I discovered in the past few days that there is at least one axiom, crucial axiom of math, missing. The missing axiom does not allow for a proper proof of Goldbach or even the Fundamental Theorem of Arithmetic, the missing axiom does not allow either one of those to be proven true, valid proof.

The missing axiom is that of Uniqueness, where a product in multiplication is unique and where a addition in math is unique.

It seems obvious to us, once we learn just a little of mathematics that 2+3 is unique and that 2*3 is unique, so obvious that no axiom in math exists to prove it. And this is what prevents the Fund. Theor or Goldbach from having a valid proof.

So, __for sure____ mathematics has a missing but essential required axiom of Uniqueness, and what that axiom states is that uniqueness arises by the pitting of addition against multiplication. So that 2+3 is unique, because 2*3 is unique.

So, I have no problem with that, however, I have a problem of whether the missing Axiom is just one missing axiom or whether we have 3 missing axioms altogether.

Axiom of Uniqueness

Axiom of Complimentarity

Axiom of Symmetry

So, I do not know at this moment whether all three are just one missing Axiom, or whether mathematics has 3 missing axioms.

We can sense that all three of those concepts are different, yet we sense there is a thread of each running through the other. You cannot have Complimentarity without having symmetry. And the uniqueness is a creation of the fact that you have compliments, for without add and multiply, two compliments, you cannot measure a uniqueness.

So I need to spend a few days trying to unravel whether math is missing 3 axioms or just 1 axiom that combines all three concepts into one. It may be the case that the concept of Complimentarity has symmetry and has uniqueness as byproducts.

Algebra has the Matrix Columns to render a clue as to whether 3 or 1.

Unfortunately, geometry should be the largest **clue center** in math, but it appears to be deaf dumb and silent on this problem. One clue is that in geometry whenever we drew a line or line segment, we always assumed, assumed falsely that it had a midpoint, had a midpoint if finite. But with a infinity borderline, we cannot make that tacit assumption anymore. For if given a finite line segment that is of distance irrational number distance, then that line segment has no midpoint. Here is where a axiom of geometry is missing. Same goes for a square with irrational number side-- does it exist at all and if so, a axiom of symmetry would weigh in.

In geometry, we always assumed, but had no valid argument that drawing a circle, that the circle can be cut with a diameter anywhere and the two halves are the same. We could never prove a statement such as that-- all we could do is say-- if someone raises that question, we call him/her crazy, was the best that Old Math could do on that.

But with a axiom of Uniqueness, Compliment, Symmetry, we could prove, or disprove a statement that all diameter cuts of a circle are equal end cut figures.

AP
Archimedes Plutonium
2017-08-11 05:53:15 UTC
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So, here, the question comes up, in order to prove Goldbach, mathematics has a missing axiom, but not only to prove Goldbach, but that Old Math has an invalid proof of Fundamental Theorem of Arithmetic, for theirs is ludicrous in thinking Euclid's Lemma proves uniqueness, the same axiom needed that is missing to prove Goldbach.

Here is the fruit-loop-crazy Old Math proof of Fundamental Theorem of Arithmetic put to shame. Their Euclid Lemma says if p is a factor of N where N = A*B then p is a factor of A or a factor of B or both. Old Math crazily thought that was a tool to prove uniqueness, crazily, because anyone can dream up a counterexample in a matter of minutes. Here is one counterexample 2*5 = 10 and 2*2*5*5 = 100. Now applying Euclid's Lemma to prove uniqueness, well, p = 5 obeys the Lemma for 10 and also for 100. And how silly the conclusion of Old Math, 10 = 100.

Uniqueness in Arithmetic cannot be established without a axiom residing in Arithmetic that tells us when and what is uniqueness.

In a different thread, I posted this::

Algebra starts with Matrix Columns Re: Old Math's missing axiom of uniqueness Re: Brand-New-Goldbach, proof of it and all its extensions

- hide quoted text -
The reason that Algebra theory, group, field, Galois etcetera, the reason that they always have add and multiply together, is because of the missing axiom that math has missed since Ancient Greek times. The missing axiom of uniqueness-- in math, the only means of measuring uniqueness-- is by the compliments of add with multiply. 2*5 is unique, because 2+5 forces 2*5 to be unique, and vice versa.
AP
Just so you know groups are only concerned with one operation, not two. Does this mean groups are fake mathematics too?
Don
When I say Group theory, I actually am sloppy, for I really mean Field theory of Algebra. Probably Ring theory is the same
Show me field theory that in the end is one operator
Quoting from Wikipedia on Ring;;

"In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra. It consists of a set equipped with two binary operations that generalize the arithmetic operations of addition and multiplication."

Now, what "abstract algebra" means is not that it is loose and airy or misty and unintelligible, or difficult and strange. What "abstract" means is that it is fundamental and what fundamental means is that it is nearby to the axioms of mathematics, close to home of what the axioms of that subject of math say and do.

So in the proof of Goldbach we come to a Matrix Column in specific of 8

0   8
1   7
2   6
3   5
4   4

and that column is all the possible ways of getting 8= a +b in Counting Numbers. All the possible ways.

So in a Goldbach proof, what happens is that the left column has to have a Bertrand Postulate prime, call it P, and the rightside column has to have another Bertrand prime call it Q, in our case it is 3 and 5. In our case, they are lined up. But, in general are the Bertrand primes lined up?

So we write the Column in general, or, as the author above would say "abstract".

0  N
1  a
2  b
3  c
4  d
.
.
.
.5N  .5N

Now, our Bertrand prime on leftside is still P and on rightside is still Q

And we come to that juncture in the proof. Now we need to say that the Bertrand prime on left lines up with the one on right. Is there anything in mathematics that guarantees they line up?

Yes, there is the guarantee from Arithmetic, that if P lines up with Q as that of P+Q = N, then the number P*Q exists. But that is a axiom that is missing in Old Math. A missing axiom that says all numbers in the Matrix Columns are unique additions and unique multiplications, because addition is the compliment of multiplication. If A*B is unique, then so is A+B is unique.

Uniqueness of product or uniqueness of sum, does not occur by some silly Lemma, such as Euclid's lemma for Fundamental Theorem of Arithmetic. Uniqueness occurs because math has a missing Axiom that says sums and products are both unique, because of this axiom.

So, in the proof of Goldbach, really a simpleton proof, is that you form Bertrand primes, then you apply axiom of uniqueness which lines up the primes. For if 3+5 did not exist, then 3*5 is nonexistent.

So, what Old Math missed was not only this Uniqueness Axiom, but missed the fact that all of Algebra starts with the display of Matrix Columns.

To start Algebra, on day one, what we start with is a display of this::
- show quoted text -
Now, those above Matrix Columns are Algebra and they show uniqueness of every addition and every multiplication, so that if a Bertrand primes P, Q exist in a Column, then P*Q exists and P+Q exists in that column, hence Goldbach proven.

So, we can say Axiom of Uniqueness, or we can say -true because of Algebra Matrix Columns.

In my proofs of Goldbach in early 1990s, I just kept saying if 3+5 does not exist, then 3*5 does not exist, violation of arithmetic, hence Goldbach.

So, what axiom was missing?

Was it just Uniqueness or was it Complimentarity, or Symmetry. Did we miss one axiom, or three?

AP
Bill
2017-08-11 06:13:06 UTC
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Post by Archimedes Plutonium
So, here, the question comes up, in order to prove Goldbach, mathematics has a missing axiom, but not only to prove Goldbach, but that Old Math
What is Old Math?
Archimedes Plutonium
2017-08-11 06:36:35 UTC
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Post by Bill
Post by Archimedes Plutonium
So, here, the question comes up, in order to prove Goldbach, mathematics has a missing axiom, but not only to prove Goldbach, but that Old Math
What is Old Math?
All math that assumed infinity = endless, assumed infinity has no borderlines between finite and infinite.

Essentially pre AP math is Old Math.

If you create any mathematics, assuming that infinity has no borders between it and finite, is flawed math, whether algebra or geometry.

Now here is a historic old post of mine in the 5th edition of Correcting Math, where 2009 is the year of Infinity borderline is discovered
--- old post of mine ---

Basically the problem with discovery of what infinity truly is, a border, had to wait until physics was more advanced than mathematics and where physics found limitations within physics itself, limitations in physics having borders such as the Uncertainty Principle, and once physics found limitations then mathematics could find borders in its subject. Infinity is a limitation.

Here are two old historically significant posts of mine where infinity border is first discussed:

Newsgroups: sci.math, sci.physics, sci.logic
From: ***@gmail.com
Date: Wed, 21 Jan 2009 18:42:07 -0800 (PST)
Local: Wed, Jan 21 2009 8:42 pm
Subject: #155 Chapter 7, set is infinite only if it contains an infinite number of "infinite specimens", and finite otherwise; new book 2nd edition: New True Mathematics

(snipped in large part)

I believe the largest number in physics is about 10^200 of the Planck
numbers, but
I have to check on that. I worked out in the 1990s that the number of
Coulomb
Interactions that keep a plutonium atom together is of the order of
192! to 231! which
are numbers larger than 10^200. I think 231! is about 10^500.

So what I propose is that since Physics is exhausted of meaning beyond
10^500,
that we peg 0000....0000999...9999 as 10^500 and thus adding 1 more to
that
delivers 0000....0001000....00000

This makes sense for in effect what I have done here is say that
Finiteness is
equivalent to being of Physics Meaning, and beyond that is the realm
of infinity
where we no longer have Physical meaning. Where we can no longer
count, and
so it makes no difference anyway since we can no longer count there.
And that is
what finite means in the first place-- it has a physics reality.

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies

Archimedes Plutonium
2017-08-11 06:20:22 UTC
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I am going to call it a short night tonight, not because of tired, but because I have too much to sort out. I need to sort out whether the missing axiom of Arithmetic, that makes Old Math's Fundamental Theorem of Arithmetic, makes it a lousy and invalid proof, whether that missing axiom is 1 , 2 or 3 axioms missing?

These three concepts are not enshrined in a axiom-- Uniqueness, Complimentary, Symmetry.

Those concepts need to arise from an axiom basis, not from a derived from other axioms and theorems.

The Old Math's alleged proof of Fundamental Theorem of Arithmetic using Euclid's Lemma is easily shown a counterexample with 2*5 = 10 and 2*2*5*5 = 100, so there is no uniqueness using Euclid's Lemma and 10=100 in Old Math.

What I need to sort out, is whether the three concepts of Uniqueness, Complementary, Symmetry are all just one concept, or do I need three separate new axioms.

One thought that may be a quick solution is to just say Matrix Column is a axiom. Call the below Matrix Column a axiom, itself, for the Matrix Column is uniqueness, is complementary of add to multiply, and is symmetrical with left right symmetry and top bottom symmetry.

So, this new axiom-- just one-- call it Matrix-Column

0  2
1  1

0  3
1  2

0  4
1  3
2  2

0  5
1  4
2  3

0  6
1  5
2  4
3  3

0  7
1  6
2  5
3  4

0  8
1  7
2  6
3  5
4  4

0  9
1  8
2  7
3  6
4  5

0  10
1   9
2   8
3   7
4   6
5   5

AP