09/29/2023, 02:30 AM
Hello!
I browsed through the thread titles, but could not find anything related. I really apologize if this has already been asked before on this forum, but, here we go:
How can I rigorously prove that, for every natural n, the limit of x tetrated to n when x approaches 0 (through the positive side) is equal to 1 if n is even and 0 if n is odd?
I tried to prove through induction, but I never manage to conclude the proof. I also searched for it, but never found the proof of this
affirmation. It is stated on this article: https://math.osu.edu/sites/math.osu.edu/...ration.pdf (page 5), and it says "evidences on the next section", but I still couldn't work it out.
Thank you.
I browsed through the thread titles, but could not find anything related. I really apologize if this has already been asked before on this forum, but, here we go:
How can I rigorously prove that, for every natural n, the limit of x tetrated to n when x approaches 0 (through the positive side) is equal to 1 if n is even and 0 if n is odd?
I tried to prove through induction, but I never manage to conclude the proof. I also searched for it, but never found the proof of this
affirmation. It is stated on this article: https://math.osu.edu/sites/math.osu.edu/...ration.pdf (page 5), and it says "evidences on the next section", but I still couldn't work it out.
Thank you.
