I waited so long to see some actual mathematics on Steemit. No hate to all the others giving out material and exercises for School-math, but as soon as I saw you split 0^0 into 0^0*0^0 I knew you would start to proof.
I actually didn't remember that 0^0 is set, maybe I also never heard it since I didnt finish college math. (Hatte nur LA 1/2 und Ana 1/2). The limis argument with x^x is very convincing, it makes a lot of sense to set 0^0=1 even if it looks strange.
I like that higher math actually has a lot more freedom. Like you can choose (set/define) to accept 0 as a natural number or you don't. Well my Profs generally tended to include it which I think is crazy, but that's another topic :D.
Also the freedom of doing the proof you can do the best and there being rarely (or even never) only one way to proof something.
Followed you and looking forward to more math like this.