- #1
pierce15
- 315
- 2
Hello all, of late I have been very interested in tetration (http://en.wikipedia.org/wiki/Tetration). I have a few questions that weren't really explained clearly by this wikipedia article. P.S., I can't get latex to work with the wikipedia notation, so I will use this notation: ##x^{\Delta n}##.
1. Why does
[tex]\lim_{n\to\infty} x^{\Delta n}[/tex] only converge for [tex]1/e<x<e^{1/e}[/tex]
2. How can the exact value be calculated as a limit? For example, how could I prove that:
[tex]\lim_{x\to\infty} \sqrt{2}^{\Delta x}=2[/tex]
3. Why is the following statement true (from the wikipedia article):
[tex]\lim_{x\to0}\lim_{n\to\infty}x^{\Delta n}=1/e[/tex]
I will be sure to post more questions as they come.
1. Why does
[tex]\lim_{n\to\infty} x^{\Delta n}[/tex] only converge for [tex]1/e<x<e^{1/e}[/tex]
2. How can the exact value be calculated as a limit? For example, how could I prove that:
[tex]\lim_{x\to\infty} \sqrt{2}^{\Delta x}=2[/tex]
3. Why is the following statement true (from the wikipedia article):
[tex]\lim_{x\to0}\lim_{n\to\infty}x^{\Delta n}=1/e[/tex]
I will be sure to post more questions as they come.
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