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 Cardinality of Infinite tetration Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 06/21/2008, 07:27 PM bo198214 Wrote: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. I have to read into this , but category theory deals with variable sets. ( I do not know if this is applicable, but seems so). There is an article in web by Prof. Bell "Abstract and variable sets in category theory". Quote:Unfortunately its not that easy, e.g: $\frac{\partial^2 x^x}{(\partial x)^2} = {{x}^{x} {\left( \ln \left( x \right) + 1 \right)}^{2} } + {x}^{x - 1}$ Thanks for correction. Anyway first differential and separated further derivatives show that there is a difference by which of x such function is differentiated, and these impact in growth speed can be separated in principle. « 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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