Originally Posted by DrRocket

No. Infinity is not undefined. It is not a real number. There are in fact different sizes of infinity -- see the theory of cardinal and ordinal numbers.

But 1/0 is simply undefined. It is not infinity. It is not anything. If 1/0 were infinity, what would 2/0 be ?

The point is that division has very clear meaning, and it implies the existence of a multiplicative inverse for whatever numbers (real numbers) are involved. Infinity is not one of them.

This is really not a debatable issue. That is how mathematics works.

You can DEFINE 1/0 to be infinity if you like, but you will have discarded the rest of mathematics if you do that.

In the theory of measure and integration is is often conveneint to work with the extended real numbers, which are the reals with +/- infinity "tacked on", and rules for addition and multiplication about as you would expect but even there 1/0 remains undefined, as is 1/(infinity).