0^0 = 1?

[Chris Dreher]

(04-24-2017 04:26 AM)Thomas Okken Wrote:  No, it's because they don't change the subject by introducing transformations that cause you to end up looking at a completely different problem.

How was the subject changed? How is it a completely different problem? What "transformations" were introduced?

(04-24-2017 04:26 AM)Thomas Okken Wrote:  Consider lim (x->0) x/x. I don't think it's controversial to say that that is 1. Now take lim (x->0) f(x)/g(x), where f(x) and g(x) are nice, well-behaved functions, both zero at x=0, both with a nonzero derivative at x=0, continuously differentiable, etc. etc. etc.

Suddenly you can make that limit come out to whatever you want. Does this lead to some deep insight? No, because you're no longer looking at the same problem.

The point above isn't clear. Can you clarify? I was with you until "Does this lead..."

Making the limit come out to whatever is desired want is one of the properties of dealing with indeterminate forms, whether dealing with 0^0 or 0/0 or 1^inf or etc. This property is why indeterminate forms do not have assigned values in general (only in some special cases).