Quote:
Originally Posted by Tolnaftate2004
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
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You are using limits to describe finite concepts. We already know 0 can be divided into 0 parts. Limit definitions are solid when finite definitions do not exist, eg diving by zero. Generally speaking, you apply the limit to the modifying operation, eg division, raising to a power, etc.