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.