>>12
No, you're completely, 100% wrong. The difference between saying 1^∞ must mean lim x->∞ of 1^x, and saying that 0/0 must mean lim x->0 of x/x is the fact that ∞ is not a number. 1^∞, as has been said before, is not a valid expression, whereas 0/0 *is* a valid expression.
>>11
You point out that 1^∞ is a valid expression on the extended number line. Ok, that's nice. Define what an exponent is in the extended number line in terms of a function. Finding it a little.. difficult? There's a reason for that.