Strange Mathematics

Normally, when we remove ‘something’ from something else, the original ‘something’ will become smaller. That is elementary mathematics.

But mathematicians have a concept called ‘infinity’ – something that has no limit, something that is not finite. Take for example, the total number of whole numbers. There are infinitely many of them – you name any number, there is another number which is larger than it.

What happens when you remove something from infinity? Will it become smaller? No, not always. It depends. Consider for example, the total number of numbers. As we saw earlier, there are infinitely many of them. What happens if we remove all even numbers from this set of numbers? You are left with infinitely many odd numbers. 

You started with something that was infinite. Removed something which was also infinite (there are infinitely many even numbers!) and what you are left with was also infinite – infinitely many odd numbers.

That means, infinity minus infinity need not be zero! It can even be infinity. Or if you ponder a bit, it can be zero or finite even!

That is strange mathematics. Isn’t it?

Even in the area of philosophy there are such strange apparent paradoxes. Let us see that next.

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