0^0 = 1?

[Thomas Okken]

(04-24-2017 03:45 AM)Chris Dreher Wrote:  So why do so many engineers, scientists, and a small number mathematicians like to say 0^0 = 1? Simply because in their respective areas they usually work with only analytic functions. Thus, they don't need to deal with the hassle of that 0^0 is actually undefined in the general case.

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.

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.