Distance formula

[Tolnaftate2004]

Originally Posted by Kristi

It doesn't matter what your calculator says, 0/0 is 0

I'm not using a calculator.

So,
lim x->0 of 0/x = 0
lim x->0+ of x/0 = infinity
lim x->0- of x/0 = -infinity
lim x->0 of x/x = 1
lim x->0 of (x/2)/x = 1/2
lim x->0 of nx/x = n (n!=0)

I know how to show 0 = 0, but how about the rest of these? How is infinity = 0? If n != 0, how is it 0, then? 0^0 or 0/0 cannot simply be described with one number.

An additional note:
lim x-> 0 of 0^x = 0
lim x-> 0 of x^0 = 1

All "modern algebra" does is lead me to believe that 0/0 is some set that includes {0,1} at least.