Thread: Concept of Quantity

Originally Posted by KAUFMANN

Any number multiplied by its inverse is 1 since N*(1/N)=1 because the N's cancel on each other. Now, since 0 is the inverse of infinity, is it safe so assume that 0*infinity=1? Methinks so.

It depends. Do you mean 0 multiplied by something that approaches infinity or something that approaches 0 multiplied by something that approaches infinity? If the former, no, it would be 0. If the latter, sometimes; It could approach anything, because it is an indeterminate form(Indeterminate form - Wikipedia, the free encyclopedia).

Originally Posted by whiteflags

inf/inf = 1
1/inf = 0
0inf = 0

lim(x->inf)x/lim(x->inf)x^2 = lim(x->inf)x/x^2 = lim(x->inf)1/x = 0
The second is correct. (I even used it above.)
lim(x->inf)1/x * lim(x->inf)x = lim(x->inf)x/x = lim(x->inf)1 = 1

The first and third are indeterminate, and can't be given a general rule.

Originally Posted by whiteflags

0 isn't the reciprocal of infinity.

inf/inf = 1
1/inf = 0
0inf = 0

All of these are made rigorous by the limit concept.

They are rigorous if you actually write them as limits. Written in the above way they are just nonsense.

Think of it this way:
Think infinity as the universe ( and ignore my signature ).
The universe is constantly expanding. Likewise, two infinities may not be the same...

I know... I think... I guess... who am I kidding?