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

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 FromTheRafters Posts: 248 Registered: 12/20/15
Re: infinity
Posted: Oct 4, 2017 5:13 PM

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.

https://en.wikipedia.org/wiki/Euclid%27s_theorem

> 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!