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Topic: Re: infinity
Replies: 27   Last Post: Dec 17, 2017 2:31 AM

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Posts: 248
Registered: 12/20/15
Re: infinity
Posted: Oct 4, 2017 7:44 PM
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Mike Terry brought next idea :
> On 04/10/2017 22:13, FromTheRafters wrote:
>> Doctor Allan explained :
>>> 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.

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