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Earlier quoted context omitted.
It doesn't, because we might consider different outputs "simple" depending on what we're going to do next.
Sure, an example would be nice.
Earlier quoted context omitted.
It also equals x with appropriate assumptions (x > 0).
Well, then sin(x) = x if x is infinitely small
Mathematica returns True. And any middle schooler will also tell you it's true.
The only reasonable interpretation of "infinitely small" is that it's zero.
Earlier quoted context omitted.
PLEASE explain "So you can extend x/x holomorphically to full C" to someone with only a BSc in math/cs; something about this thread is giving me an existential crisis right now.
- function extension is defining a function where it is not defined - function extension is an extension that keeps (or gives) Adj property - extended function is usually treated as originals if extension is good enough. Real analysis starts with defining real numbers and extending familiar functions onto them - in this particular case we do not need C - even continuous extension on R works and agrees with x/x = 1 at…