b implies a, so you could shorten your list, if you want.

In general, aren't all decimal expansions infinite sums? Decimal representation - Wikipedia, the free encyclopedia

What makes equations that involve infinity wrong?

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- 03-17-2011User Name:
b implies a, so you could shorten your list, if you want.

In general, aren't all decimal expansions infinite sums? Decimal representation - Wikipedia, the free encyclopedia

What makes equations that involve infinity wrong? - 03-31-2011KAUFMANN
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.

- 03-31-2011whiteflags
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. - 03-31-2011brewbuck
- 04-01-2011GReaper
Think of it this way:

Think infinity as the universe ( and ignore my signature :D ).

The universe is constantly expanding. Likewise, two infinities may not be the same...

I know... I think... I guess... who am I kidding? :D - 04-01-2011Mario F.
Except 0. Otherwise...

0 * (1/0) = 1

Quote:

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.

- 04-01-2011User Name:
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).

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.