To Infinity and Beyond

Posted: 19.03.09 in Blogging

One of my heroes is Georg Cantor. The branch of mathematics that he (pretty much) invented himself goes some way to proving the point I was making yesterday.

If I were to ask you to count to infinity, what number would you start on? And what would be your next number?

Cantor thought about it. If you count the Natural numbers (that is 1, 2, 3, …) then you will eventually count to infinity. But if you count all the integers, including minus numbers as well, (0, 1, -1, 2, -2, …) then you will count infinitely many numbers again: but surely you will have counted more numbers this way.

If you keep changing the way you count, you can begin to see that you count a different infinity each time. In theory, there are an infinite number of infinities. That sounds odd, doesn’t it?!


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