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 Additional super exponential condition bo198214 Administrator Posts: 1,386 Threads: 90 Joined: Aug 2007 10/13/2008, 07:15 PM I was just thinking about the following for an arbitrary super exponential $\text{sexp}$: We surely have for natural numbers m and n that $\text{sexp}(n+m)\ge \text{sexp}(n) ^ {\text{sexp}(m)}$ So why not demand this rule also for the super exponential extended to the reals? For a super logarithm the rule would be: $\text{slog}(x^y) \le \text{slog}(x) + \text{slog}(y)$ Note that this rule is not applicable to the left-bracketed super exponentials. Because from the rule it follows already that: $\text{sexp}(n)\ge \exp^{\circ n}(1)$ which is not valid for left bracketed super exponentials because they grow more slowly. I didnt verify the rule yet for our known tetration extensions. Do you think it will be valid? However I dont think that this condition suffice as a uniqueness criterion. But at least it would reduce the set of valid candidates. « Next Oldest | Next Newest »

 Messages In This Thread Additional super exponential condition - by bo198214 - 10/13/2008, 07:15 PM RE: Additional super exponential condition - by andydude - 10/14/2008, 08:11 PM RE: Additional super exponential condition - by martin - 10/21/2008, 03:40 PM

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