Doctor Allan

2017-10-04 20:30:15 UTC

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! 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!

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! 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!