Discussion:
infinity
Doctor Allan
2017-10-04 20:30:15 UTC
does infinity exists and if so how can i prove it by math ?

Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.

What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.

x=2*3*5*7*...*lastprime+1.

x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.

Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
FromTheRafters
2017-10-04 21:13:42 UTC
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a
concept of "stone"--imagine "stone"; you know what this concept means,
because you can find examples of it, but no single example is the actual
gestalt. Just like the concept of "one", "infinity" is not a standalone
object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as
another poster has recounted. A simple one is a proof of the infinity of the
number of prime numbers. 2,3,5,7.... Let's see what happens if we assume
the number of primes is finite. Let's see what we get when we multiply them
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring
it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime
leaves a remainder of 1, so x must be prime!
As I understand the proof, this is wrong. It means x is *either* prime
or is a composite number with at least one of its prime factors not on
the list.

https://en.wikipedia.org/wiki/Euclid%27s_theorem
Post by Doctor Allan
that we have only a finite number of primes, as x was created by multiplying
by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a
line segment and also draw next to it (not connected to it) a circle. Put
your pencil now over one end of the line segment and trace the entire path,
stopping when you get to the end. As you can tell, the maximum path length
is exactly what you think--finite. Now try this with a circle. Notice that
you can smoothly move your pencil round and round and round the circle
without ever coming to an end. Like a treadmill, the maximum path length on
a circuit is infinite. This is useful, for track, car, horse, dog races and
also for gyms, that they can provide a track that will allow for more than
any finite distance. This, my friend, is an example of infinity you can
point at!
Mike Terry
2017-10-04 23:06:31 UTC
Post by FromTheRafters
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there
is a concept of "stone"--imagine "stone"; you know what this concept
means, because you can find examples of it, but no single example is
the actual gestalt. Just like the concept of "one", "infinity" is not
a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in
mathematics, as another poster has recounted. A simple one is a proof
of the infinity of the number of prime numbers. 2,3,5,7.... Let's
see what happens if we assume the number of primes is finite. Let's
see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try
factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in
fact, x/any-prime leaves a remainder of 1, so x must be prime!
As I understand the proof, this is wrong. It means x is *either* prime
or is a composite number with at least one of its prime factors not on
the list.
The list contained ALL the prime numbers, on the assumption that there
were only finitely many of them. So x has no prime factors less than
itself, and so must be prime. This establishes a contradition, as it is
greater than all the numbers in the list, and hence also is not a prime.
So we conclude there are infinitely many primes...)

Regards,
Mike.
FromTheRafters
2017-10-04 23:44:08 UTC
Post by FromTheRafters
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there
is a concept of "stone"--imagine "stone"; you know what this concept
means, because you can find examples of it, but no single example is
the actual gestalt. Just like the concept of "one", "infinity" is not
a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in
mathematics, as another poster has recounted. A simple one is a proof
of the infinity of the number of prime numbers. 2,3,5,7.... Let's
see what happens if we assume the number of primes is finite. Let's
see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try
factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in
fact, x/any-prime leaves a remainder of 1, so x must be prime!
As I understand the proof, this is wrong. It means x is *either* prime
or is a composite number with at least one of its prime factors not on
the list.
The list contained ALL the prime numbers, on the assumption that there were
only finitely many of them. So x has no prime factors less than itself, and
so must be prime. This establishes a contradition, as it is greater than all
the numbers in the list, and hence also is not a prime. So we conclude
there are infinitely many primes...)
Regards,
Mike.
I understand that, but there are other lists of primes possible which
one can assume to be *all* of them. Those interested might enjoy this
whole lecture, but I copied it starting at the relevant part.

FromTheRafters
2017-10-05 03:03:16 UTC
Post by FromTheRafters
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there
is a concept of "stone"--imagine "stone"; you know what this concept
means, because you can find examples of it, but no single example is
the actual gestalt. Just like the concept of "one", "infinity" is not
a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in
mathematics, as another poster has recounted. A simple one is a proof
of the infinity of the number of prime numbers. 2,3,5,7.... Let's
see what happens if we assume the number of primes is finite. Let's
see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try
factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in
fact, x/any-prime leaves a remainder of 1, so x must be prime!
As I understand the proof, this is wrong. It means x is *either* prime
or is a composite number with at least one of its prime factors not on
the list.
The list contained ALL the prime numbers, on the assumption that there were
only finitely many of them. So x has no prime factors less than itself,
and so must be prime. This establishes a contradition, as it is greater
than all the numbers in the list, and hence also is not a prime. So we
conclude there are infinitely many primes...)
Regards,
Mike.
I understand that, but there are other lists of primes possible which one can
assume to be *all* of them. Those interested might enjoy this whole lecture,
but I copied it starting at the relevant part.
http://youtu.be/lzyWL1LTlq4
Here, replying to myself because I can provide a quote from another
source:

"It is a common mistake to think that this proof says the product
p1p2...pr+1 is prime. The proof actually only uses the fact that there
is a prime dividing this product (see primorial primes)."

From:

https://primes.utm.edu/notes/proofs/infinite/euclids.html
Mike Terry
2017-10-05 04:07:54 UTC
Post by FromTheRafters
Post by FromTheRafters
Post by Mike Terry
Post by FromTheRafters
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there
is a concept of "stone"--imagine "stone"; you know what this concept
means, because you can find examples of it, but no single example is
the actual gestalt. Just like the concept of "one", "infinity" is not
a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in
mathematics, as another poster has recounted. A simple one is a proof
of the infinity of the number of prime numbers. 2,3,5,7.... Let's
see what happens if we assume the number of primes is finite. Let's
see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try
factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in
fact, x/any-prime leaves a remainder of 1, so x must be prime!
As I understand the proof, this is wrong. It means x is *either* prime
or is a composite number with at least one of its prime factors not on
the list.
The list contained ALL the prime numbers, on the assumption that
there were only finitely many of them. So x has no prime factors
less than itself, and so must be prime. This establishes a
contradition, as it is greater than all the numbers in the list, and
hence also is not a prime. So we conclude there are infinitely many
primes...)
Regards,
Mike.
I understand that, but there are other lists of primes possible which
one can assume to be *all* of them. Those interested might enjoy this
whole lecture, but I copied it starting at the relevant part.
http://youtu.be/lzyWL1LTlq4
"It is a common mistake to think that this proof says the product
p1p2...pr+1 is prime. The proof actually only uses the fact that there
is a prime dividing this product (see primorial primes)."
https://primes.utm.edu/notes/proofs/infinite/euclids.html
That's all well and good, but again this is a comment specifically on
Euclid's proof, or some specific variation of that proof. The link you
give is not talking about the OP's proof, and certainly does not know
what the OP was thinking for the justification for claiming that x (in
the OP's proof) is prime. The links are NOT saying the OP's proof is
"wrong", which seems to be what you're suggesting.

Do you accept:

a) that IF the OP had managed to supply a valid reasoning
for x being prime, then the OP's proof would be valid.
(You may think no such reasoning exists, but that's not
the question here)

b) that there are a number of such valid reasonings available,
although (we agree) the OP did not supply any of them

?

Mike.
FromTheRafters
2017-10-05 07:30:49 UTC
Post by Mike Terry
Post by FromTheRafters
Post by FromTheRafters
Post by Mike Terry
Post by FromTheRafters
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there
is a concept of "stone"--imagine "stone"; you know what this concept
means, because you can find examples of it, but no single example is
the actual gestalt. Just like the concept of "one", "infinity" is not
a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in
mathematics, as another poster has recounted. A simple one is a proof
of the infinity of the number of prime numbers. 2,3,5,7.... Let's
see what happens if we assume the number of primes is finite. Let's
see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try
factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in
fact, x/any-prime leaves a remainder of 1, so x must be prime!
As I understand the proof, this is wrong. It means x is *either* prime
or is a composite number with at least one of its prime factors not on
the list.
The list contained ALL the prime numbers, on the assumption that
there were only finitely many of them. So x has no prime factors
less than itself, and so must be prime. This establishes a
contradition, as it is greater than all the numbers in the list, and
hence also is not a prime. So we conclude there are infinitely many
primes...)
Regards,
Mike.
I understand that, but there are other lists of primes possible which
one can assume to be *all* of them. Those interested might enjoy this
whole lecture, but I copied it starting at the relevant part.
http://youtu.be/lzyWL1LTlq4
"It is a common mistake to think that this proof says the product
p1p2...pr+1 is prime. The proof actually only uses the fact that there
is a prime dividing this product (see primorial primes)."
https://primes.utm.edu/notes/proofs/infinite/euclids.html
That's all well and good, but again this is a comment specifically on
Euclid's proof, or some specific variation of that proof. The link you give
is not talking about the OP's proof, and certainly does not know what the OP
was thinking for the justification for claiming that x (in the OP's proof) is
prime. The links are NOT saying the OP's proof is "wrong", which seems to be
what you're suggesting.
a) that IF the OP had managed to supply a valid reasoning
for x being prime, then the OP's proof would be valid.
(You may think no such reasoning exists, but that's not
the question here)
b) that there are a number of such valid reasonings available,
although (we agree) the OP did not supply any of them
?
Mike.
Okay, I guess. Still, it seems to me that stipulating a 'lastprime'
rather than an n^th prime where n is a natural (finite) number is not
valid. It is like saying you have an actual last natural number as an
index. This leaves out the 'headroom' needed to make my assertion
correct.

That seems to be the only difference between this and Euclid's proof,
hence my comment. Maybe the OP will chime in and make this clearer.
Mike Terry
2017-10-05 03:46:46 UTC
Post by FromTheRafters
Post by Mike Terry
Post by FromTheRafters
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there
is a concept of "stone"--imagine "stone"; you know what this concept
means, because you can find examples of it, but no single example is
the actual gestalt. Just like the concept of "one", "infinity" is not
a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in
mathematics, as another poster has recounted. A simple one is a proof
of the infinity of the number of prime numbers. 2,3,5,7.... Let's
see what happens if we assume the number of primes is finite. Let's
see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try
factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in
fact, x/any-prime leaves a remainder of 1, so x must be prime!
As I understand the proof, this is wrong. It means x is *either* prime
or is a composite number with at least one of its prime factors not on
the list.
The list contained ALL the prime numbers, on the assumption that there
were only finitely many of them. So x has no prime factors less than
itself, and so must be prime. This establishes a contradition, as it
is greater than all the numbers in the list, and hence also is not a
prime. So we conclude there are infinitely many primes...)
Regards,
Mike.
I understand that, but there are other lists of primes possible which
one can assume to be *all* of them. Those interested might enjoy this
whole lecture, but I copied it starting at the relevant part.
http://youtu.be/lzyWL1LTlq4
I don't get the point you're trying to make re "other lists of primes".
The link points to a YouTube clip of someone running through the
standard Euclid's proof, which is fine, but doesn't make the OP's proof
"wrong".

I suppose we could criticise the OP for not providing the detailed
justification as to why x (in the OP's proof) must be prime, but in
fairness I don't think the OP intended to give a complete/formal proof!
Most proofs in practice miss out simple steps that the author thinks
will be readily filled in by the reader. That's why I supplied an
acceptable justification, which assumes we've previously proved the result:

If a number n>1 has no prime factor smaller than n,
then n is prime.

With this extra justification the OP's proof is OK, so I wouldn't say
the proof was wrong, just that it wasn't complete.

Anyway, that's what I *guessed* the OP would have said if challenged,
but perhaps he/she had some other reasoning - having constructed x there
are multiple paths we can take to show a contradiction, and they are all
OK.

E.g. another approach could be to use a simple result:

Every number n>1 is divisible by some prime number.

(Clearly we can show the OP's x is not divisible by any prime number,
since it leaves a remainder of 1 when divided by every prime:

Hmmm, interesting that doing it like this we don't need to have
previously proved the uniqueness of prime factorisations, just their
*existence*, so perhaps that's an advantage for this approach...

I guess it's also possible that the OP did not have in mind a correct
reasoning as to why x must be prime, in which case the OP was making a
mistake in claiming to have a proof! :)

Mike.
Conway
2017-10-04 23:54:47 UTC
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
I will take this a step further

Math proves infinite exists

Only one word works to describe God in totality...

Infinite

Therefore...math proves God's existence.
m***@gmail.com
2017-10-05 00:37:51 UTC
Post by Conway
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
I will take this a step further
Math proves infinite exists
By the Continuum Hypothesis...
We are stuck with sum largest quantity
no matter what.
We cannot calculate to infinity.
Unlimited quantity is a definition.
The Continuum Hypothesis works.
Post by Conway
Only one word works to describe God in totality...
Infinite
But He is more than that...
Post by Conway
Therefore...math proves God's existence.
There is order before man's mind...

Mitchell Raemsch
Conway
2017-10-05 00:49:20 UTC
Post by m***@gmail.com
Post by Conway
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
I will take this a step further
Math proves infinite exists
By the Continuum Hypothesis...
We are stuck with sum largest quantity
no matter what.
We cannot calculate to infinity.
Unlimited quantity is a definition.
The Continuum Hypothesis works.
Post by Conway
Only one word works to describe God in totality...
Infinite
But He is more than that...
Post by Conway
Therefore...math proves God's existence.
There is order before man's mind...
Mitchell Raemsch
Surely you just wish to argue.

Cleary you understood that I meant by using the word "Infinite"...."all that is"
Just as there is unique kinds of infinites...there is only one "total" infinite....

In any case...say I'm wrong.....if you say he is more than infinite...well then I agree....because what I meant by infinite was "all that is"...abstract or otherwise...apriori or empirical...existentialism and consciousness....

lastly...I apologize to the op...as this will probably be a derailing of his/her post.........
m***@gmail.com
2017-10-05 01:05:48 UTC
Post by Conway
Post by m***@gmail.com
Post by Conway
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
I will take this a step further
Math proves infinite exists
By the Continuum Hypothesis...
We are stuck with sum largest quantity
no matter what.
We cannot calculate to infinity.
Unlimited quantity is a definition.
The Continuum Hypothesis works.
Post by Conway
Only one word works to describe God in totality...
Infinite
But He is more than that...
Post by Conway
Therefore...math proves God's existence.
There is order before man's mind...
Mitchell Raemsch
Surely you just wish to argue.
I like to express what I believe...
Don't you? The continuum hypothesis
uses infinity in an understandable way.
We cannot Calculate To It so you are correct
in that way.

Mitchell Raemsch
Post by Conway
Cleary you understood that I meant by using the word "Infinite"...."all that is"
Just as there is unique kinds of infinites...there is only one "total" infinite....
In any case...say I'm wrong.....if you say he is more than infinite...well then I agree....because what I meant by infinite was "all that is"...abstract or otherwise...apriori or empirical...existentialism and consciousness....
lastly...I apologize to the op...as this will probably be a derailing of his/her post.........
Zelos Malum
2017-10-05 04:26:57 UTC
Post by m***@gmail.com
Post by Conway
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
I will take this a step further
Math proves infinite exists
By the Continuum Hypothesis...
We are stuck with sum largest quantity
no matter what.
We cannot calculate to infinity.
Unlimited quantity is a definition.
The Continuum Hypothesis works.
Post by Conway
Only one word works to describe God in totality...
Infinite
But He is more than that...
Post by Conway
Therefore...math proves God's existence.
There is order before man's mind...
Mitchell Raemsch
Can you please shut up about the continuum hypothesis? You have no clue what it says.
m***@gmail.com
2017-10-05 04:46:29 UTC
Post by Zelos Malum
Post by m***@gmail.com
Post by Conway
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
I will take this a step further
Math proves infinite exists
By the Continuum Hypothesis...
We are stuck with sum largest quantity
no matter what.
We cannot calculate to infinity.
Unlimited quantity is a definition.
The Continuum Hypothesis works.
Post by Conway
Only one word works to describe God in totality...
Infinite
But He is more than that...
Post by Conway
Therefore...math proves God's existence.
There is order before man's mind...
Mitchell Raemsch
Can you please shut up about the continuum hypothesis? You have no clue what it says.
A size of an infinity of the infinitely small creates finite integers.

Mitchell Raemsch
Zelos Malum
2017-10-05 05:23:06 UTC
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Conway
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
I will take this a step further
Math proves infinite exists
By the Continuum Hypothesis...
We are stuck with sum largest quantity
no matter what.
We cannot calculate to infinity.
Unlimited quantity is a definition.
The Continuum Hypothesis works.
Post by Conway
Only one word works to describe God in totality...
Infinite
But He is more than that...
Post by Conway
Therefore...math proves God's existence.
There is order before man's mind...
Mitchell Raemsch
Can you please shut up about the continuum hypothesis? You have no clue what it says.
A size of an infinity of the infinitely small creates finite integers.
Mitchell Raemsch
That has nothign to do with continuum hypothesis, for fuck sake, just go to wikipedia and read what it says!
m***@gmail.com
2017-10-05 06:25:22 UTC
Post by Zelos Malum
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Conway
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
I will take this a step further
Math proves infinite exists
By the Continuum Hypothesis...
We are stuck with sum largest quantity
no matter what.
We cannot calculate to infinity.
Unlimited quantity is a definition.
The Continuum Hypothesis works.
Post by Conway
Only one word works to describe God in totality...
Infinite
But He is more than that...
Post by Conway
Therefore...math proves God's existence.
There is order before man's mind...
Mitchell Raemsch
Can you please shut up about the continuum hypothesis? You have no clue what it says.
A size of an infinity of the infinitely small creates finite integers.
Mitchell Raemsch
That has nothign to do with continuum hypothesis, for fuck sake, just go to wikipedia and read what it says!
How are you sure wakipedia is right?
You can't believe everything you read.

Mitchell Raemsch
Zelos Malum
2017-10-05 08:59:02 UTC
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Conway
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
I will take this a step further
Math proves infinite exists
By the Continuum Hypothesis...
We are stuck with sum largest quantity
no matter what.
We cannot calculate to infinity.
Unlimited quantity is a definition.
The Continuum Hypothesis works.
Post by Conway
Only one word works to describe God in totality...
Infinite
But He is more than that...
Post by Conway
Therefore...math proves God's existence.
There is order before man's mind...
Mitchell Raemsch
Can you please shut up about the continuum hypothesis? You have no clue what it says.
A size of an infinity of the infinitely small creates finite integers.
Mitchell Raemsch
That has nothign to do with continuum hypothesis, for fuck sake, just go to wikipedia and read what it says!
How are you sure wakipedia is right?
You can't believe everything you read.
Mitchell Raemsch
Because I have read it elsewhere in other sources and wikipedia is correct on it. For fuck sake
Dan Christensen
2017-10-05 02:18:56 UTC
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Whether a set is finite or infinite is an important distinction. Do you agree? Or is that not what you are getting at?

Dan
Markus Klyver
2017-10-05 13:20:57 UTC
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
There is a long list of "infinities (with no claim to exhaustiveness):
infinity of the one-point compactification of N,
infinity of the one-point compactification of R,
infinity of the two-point compactification of R,
infinity of the one-point compactification of C,
infinities of the projective extension of the plane,
infinity of Lebesgue-type integration theory,
infinities of the non-standard extension of R,
infinities of the theory of ordinal numbers,
infinities of the theory of cardinal numbers,
infinity adjoined to normed spaces, whose neighborhoods are
complements of relatively compact sets,
infinity adjoined to normed spaces, whose neighborhoods are
complements of bounded sets,
infinity around absolute G-delta non-compact metric spaces,
infinity in the theory of convex optimization,
etc.;

each of these has a clear definition and a set of well-defined rules
for handling it. In mathematics, the textbook definitions applies. And definitions can vary from textbook to textbook and from field to field. For example, "dimension" has several meanings in mathematics. The same can be said about different notions of infinity, as above.
Peter Percival
2017-10-05 13:28:04 UTC
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Usually by an axiom that claims that a set, let's call it "X", exists
and a definition that says "in infinite set is one that...". And it
turns out that X satisfies that definition.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
m***@gmail.com
2017-10-05 20:02:53 UTC
Post by Peter Percival
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Usually by an axiom that claims that a set, let's call it "X", exists
and a definition that says "in infinite set is one that...". And it
turns out that X satisfies that definition.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
If we calculate forever we never reach infinity... only
some increasing largest quantity.
Zelos Malum
2017-10-06 05:38:59 UTC
Post by m***@gmail.com
Post by Peter Percival
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Usually by an axiom that claims that a set, let's call it "X", exists
and a definition that says "in infinite set is one that...". And it
turns out that X satisfies that definition.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
If we calculate forever we never reach infinity... only
some increasing largest quantity.
And how is that remotely relevant?
m***@gmail.com
2017-12-16 00:33:48 UTC
Post by Zelos Malum
Post by m***@gmail.com
Post by Peter Percival
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Usually by an axiom that claims that a set, let's call it "X", exists
and a definition that says "in infinite set is one that...". And it
turns out that X satisfies that definition.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
If we calculate forever we never reach infinity... only
some increasing largest quantity.
And how is that remotely relevant?
Calculus in real world curves cannot calculate
to the absolute exact. It can only approach.
Zelos Malum
2017-12-16 02:17:56 UTC
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Peter Percival
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Usually by an axiom that claims that a set, let's call it "X", exists
and a definition that says "in infinite set is one that...". And it
turns out that X satisfies that definition.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
If we calculate forever we never reach infinity... only
some increasing largest quantity.
And how is that remotely relevant?
Calculus in real world curves cannot calculate
to the absolute exact. It can only approach.
This is mathematics, not reality.
m***@gmail.com
2017-12-16 02:47:17 UTC
Post by Zelos Malum
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Peter Percival
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Usually by an axiom that claims that a set, let's call it "X", exists
and a definition that says "in infinite set is one that...". And it
turns out that X satisfies that definition.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
If we calculate forever we never reach infinity... only
some increasing largest quantity.
And how is that remotely relevant?
Calculus in real world curves cannot calculate
to the absolute exact. It can only approach.
This is mathematics, not reality.
Math can be real... I don't know about you...

Mitchell Raemsch
Zelos Malum
2017-12-16 07:31:25 UTC
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Peter Percival
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Usually by an axiom that claims that a set, let's call it "X", exists
and a definition that says "in infinite set is one that...". And it
turns out that X satisfies that definition.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
If we calculate forever we never reach infinity... only
some increasing largest quantity.
And how is that remotely relevant?
Calculus in real world curves cannot calculate
to the absolute exact. It can only approach.
This is mathematics, not reality.
Math can be real... I don't know about you...
Mitchell Raemsch
But mathematics is not about reality or dependent on reality. It is logic.
m***@gmail.com
2017-12-16 20:37:01 UTC
Post by Zelos Malum
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Peter Percival
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Usually by an axiom that claims that a set, let's call it "X", exists
and a definition that says "in infinite set is one that...". And it
turns out that X satisfies that definition.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
If we calculate forever we never reach infinity... only
some increasing largest quantity.
And how is that remotely relevant?
Calculus in real world curves cannot calculate
to the absolute exact. It can only approach.
This is mathematics, not reality.
Math can be real... I don't know about you...
Mitchell Raemsch
But mathematics is not about reality or dependent on reality. It is logic.
Logic is real and mathematics applies to all physicality.

Mitchell Raemsch
bassam king karzeddin
2017-12-17 07:31:55 UTC
Post by Zelos Malum
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Zelos Malum
Post by m***@gmail.com
Post by Peter Percival
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Usually by an axiom that claims that a set, let's call it "X", exists
and a definition that says "in infinite set is one that...". And it
turns out that X satisfies that definition.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
If we calculate forever we never reach infinity... only
some increasing largest quantity.
And how is that remotely relevant?
Calculus in real world curves cannot calculate
to the absolute exact. It can only approach.
This is mathematics, not reality.
Math can be real... I don't know about you...
Mitchell Raemsch
But mathematics is not about reality or dependent on reality. It is logic.
And anything that is independent of existing reality is certainly fictional and unreal encluding the logic OR the mathematics they follow, for sure
BKK
bassam king karzeddin
2018-02-12 14:16:26 UTC
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
Are you still a believer in infinity? wonder!

BKK
bassam king karzeddin
2018-02-20 15:54:34 UTC
Post by Doctor Allan
does infinity exists and if so how can i prove it by math ?
Infinity is a concept based on observation, in the same way as there is a concept of "stone"--imagine "stone"; you know what this concept means, because you can find examples of it, but no single example is the actual gestalt. Just like the concept of "one", "infinity" is not a standalone object, but a descriptive concept.
What does it mean? Well, there are many meanings, even in mathematics, as another poster has recounted. A simple one is a proof of the infinity of the number of prime numbers. 2,3,5,7.... Let's see what happens if we assume the number of primes is finite. Let's see what we get when we multiply them all together and add one.
x=2*3*5*7*...*lastprime+1.
x is clearly larger than all the primes. Is x a prime? Let's try factoring it! x/2 leaves remainder 1, x/3 leaves remainder 1... in fact, x/any-prime leaves a remainder of 1, so x must be prime! But this contradicts the idea that we have only a finite number of primes, as x was created by multiplying by all of them. Therefore, the number of primes is infinite.
Now you may want to see an example of infinity in the real world. Draw a line segment and also draw next to it (not connected to it) a circle. Put your pencil now over one end of the line segment and trace the entire path, stopping when you get to the end. As you can tell, the maximum path length is exactly what you think--finite. Now try this with a circle. Notice that you can smoothly move your pencil round and round and round the circle without ever coming to an end. Like a treadmill, the maximum path length on a circuit is infinite. This is useful, for track, car, horse, dog races and also for gyms, that they can provide a track that will allow for more than any finite distance. This, my friend, is an example of infinity you can point at!
hey Dr. allan, are you still a sincere believer of infinity? wonder!

Say it loudly again,

BKK
Zelos Malum
2018-02-21 08:43:15 UTC