Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Re: infinity
Replies: 21   Last Post: Oct 6, 2017 1:38 AM

 Messages: [ Previous | Next ]
 Mike Terry Posts: 750 Registered: 12/6/04
Re: infinity
Posted: Oct 4, 2017 7:06 PM

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.