
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/anyprime 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.

