The Math Forum

Search All of the Math Forum:

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

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 248
Registered: 12/20/15
Re: infinity
Posted: Oct 4, 2017 5:13 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

> 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!

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.