06/28/2010, 11:34 PM
Thank you for your reply and for the thread link.
It has been obvious to me that for tetrations:![[Image: mimetex.cgi?%7B%5Ea(%5Ebx)%7D\neq%7B%5E%7Bab%7Dx%7D]](http://math.eretrandre.org/cgi-bin/mimetex.cgi?%7B%5Ea(%5Ebx)%7D\neq%7B%5E%7Bab%7Dx%7D)
is a correct statement. But it has not been obvious to me that: ![[Image: n%7D%7D(%7B%5E%7Bn%7Dx)\neq%20x]](http://math.eretrandre.org/cgi-bin/mimetex.cgi?%7B%5E%7B1/n%7D%7D(%7B%5E%7Bn%7Dx)\neq%20x)
which from the thread is said to be the case because the above property (1st eq.) isn't an equality then you can not assume that ![[Image: n%7D%7D(%7B%5E%7Bn%7Dx)=x]](http://math.eretrandre.org/cgi-bin/mimetex.cgi?%7B%5E%7B1/n%7D%7D(%7B%5E%7Bn%7Dx)=x)
. Therefore this means that you can not define ![[Image: n%7Dx]](http://math.eretrandre.org/cgi-bin/mimetex.cgi?%7B%7D%5E%7B1/n%7Dx)
to be the "super-root of order 'n' " and consequentially one doesn't even know what defines (i.e. evaluates to).
ARE non-integer tetrations defined (not in interpolative methods that is)? Also without making any extra assumptions.
Btw, is there a better way to write TeX in here? I have to keep using "Insert Image" and referring to mimetex.cgi to do this.
It has been obvious to me that for tetrations:
ARE non-integer tetrations defined (not in interpolative methods that is)? Also without making any extra assumptions.
Btw, is there a better way to write TeX in here? I have to keep using "Insert Image" and referring to mimetex.cgi to do this.