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.