maths

infinity isn't a number.

The lim (1/x) as x→0 = ∞.

Or the lim (1/x) as x→ ∞ = 0

Rap

I believe that the first, lim(1/x) as x->0 = undefined. For a limit to defined, doesn't it need to be defined at the limit you're looking for? And the second is misleading. Infinity in this case is "increasing without bound" and when used in an integral represents the entirety.

I think we're arguing from the opposite sides of the same page as infinity isn't really a defined number.

Nevertheless, if one looks at division by increasingly small or large numbers the result is the aforementioned events.

Granted, it's somewhat of a personal interpertation, but it is one that has worked for me.

Rap

Vengo,

Rapraps first limit is absolutely correct. The limit of (1/x) as x approaches 0 is infinity. It is not undefined.

Punit,

There is a reason that 0 * infinity is undefined. If it isn't, it leads to impossible contradiction.

Try these

What is 1 * infinity?

What is 2 * infinity?

What is 3/infinity?

What is (3 / infinity) * infinity?

Do you see the problem?

No. That's kind of the point sometimes.