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 Cardinality of Infinite tetration bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 06/20/2008, 09:18 PM Ivars Wrote:bo198214 Wrote:What is |x[4]2|? I was not aware that x[4]2 is a set. Hmm. I thought it can be perceived as set by analogy to n^n which is a set of all permutations of n from n with order and repetitions. Whatever, but $n$ is a variable so you can regard $5^5$ as a set in this sense but not $n^n$ or $x^x$ as it depends on $n$ or $x$ respectively. Quote:Then next derivatives and their general form are easy to see: $x^{(x-n)}*x+x^{x}*(\ln(x))^n=x^{x-n+1}+x^{x}*(\ln(x))^n$ Unfortunately its not that easy, e.g: $\frac{\partial^2 x^x}{(\partial x)^2} = {{x}^{x} {\left( \ln \left( x \right) + 1 \right)}^{2} } + {x}^{x - 1}$ « Next Oldest | Next Newest »

 Messages In This Thread Cardinality of Infinite tetration - by Ivars - 06/17/2008, 01:02 PM RE: Cardinality of Infinite tetration - by Ivars - 06/17/2008, 07:59 PM RE: Cardinality of Infinite tetration - by andydude - 06/17/2008, 08:52 PM RE: Cardinality of Infinite tetration - by Ivars - 06/18/2008, 08:12 AM RE: Cardinality of Infinite tetration - by bo198214 - 06/20/2008, 02:16 PM RE: Cardinality of Infinite tetration - by Ivars - 06/20/2008, 04:28 PM RE: Cardinality of Infinite tetration - by bo198214 - 06/20/2008, 09:18 PM RE: Cardinality of Infinite tetration - by Ivars - 06/21/2008, 07:27 PM RE: Cardinality of Infinite tetration - by Ivars - 07/13/2008, 08:07 PM

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