0^0 = 1?

[Chris Dreher]

(04-22-2017 01:02 AM)Egan Ford Wrote:  

(04-21-2017 01:54 PM)Thomas Okken Wrote:  Given that, setting 0^0=NaN but 0.^0.=1. doesn't seem to make sense.

lim x->0 f(x)^g(x) = 1, if f(x), g(x) are real functions perhaps? 0. is real.

There are some real functions f(x) and g(x) where lim x->0 f(x)^g(x) does not equal 1. I remember coming up with some back in my college days when "0^0" was being debated by students (almost a quarter century ago). Initially, I sided with the students that 0^0=1 (the HP 48SX being supporting evidence). However, by the next class I thought of some formulas that supported the professor's correct statement that 0^0 is of Indeterminate Form.

https://en.wikipedia.org/wiki/Indeterminate_form