# Infinity

## Infinity.

Infinity is the term used to describe something with no end.
Most of us should have known this since elementary school.
However, what many do not know is that there are different kinds of infinity.

Try this:

Imagine a standard 12-inch ruler. If I asked you to tell me how many times you could divide the space between the number 0 and the number 1 on the ruler, you would reply “Well, I could keep dividing that space forever..” and you would be correct.
There are an infinite number of real numbers between 0 and 1.

Imagine the same 12-inch ruler. If I asked you how many times you could divide the space between the number 0 and the number 12, what would you say? Again, the answer is infinity. However, it is obvious that this infinity is MUCH larger than the infinity located between 0 and 1.

There are an infinite number of real numbers between 0 and 1. There are 12 times as many real numbers from 0 to 12.

So how do we distinguish between different sized infinities?
We can just call one set of data “infinity” and call another set of data a “larger infinity”.

http://en.wikipedia.org/wiki/Infinity

And yes, Blowfish.’s post reminded of this.

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One Response to “Infinity”
1. Avrila Klaus Says...

On August 7, 2012 at 7:35 pm

On the other hand, since both are infinite, you can set up a one-to-one correspondence between them — for example, the point n% of the way along between 0 and 1 can go to the point n% of the way along between 0 and 12. And if sets have a one-to-one correspondence, they must be the same size.

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