On 17 avr, 00:49, "Gabriel Genellina" <[EMAIL PROTECTED]> wrote: > En Wed, 16 Apr 2008 19:21:18 -0300, John Machin <[EMAIL PROTECTED]> > escribió: > > > [EMAIL PROTECTED] wrote: > >> also i found a link which states 0^0 isnt 1 even though every > >> calculator ive tried says it is. > >> it doesnt say what it is but i presume 0 then. > >> but it seems the dude is wrong and it is 1? > > > Of the possible results of 0 ** 0 (i.e. 1, 0, and NaN), 1 seems to be > > the least implausible. It allows X ** 0 to be 1 for all X. > > But a result of 0 would allow 0 ** X to be 0 for all X. (btw, this is the > reason lim(x**x) for x->0 does not exist)
lim(x**x) for x->0+ is well defined, exists and equals 1. [1] As x**x is continuous in 0+, it is widely customary to have: 0**0:=1 [1] Recall that x**x := exp(x*log(x)) The limit of x*log(x) for x->0 is 0 [2] therefore lim(x**x) for x->0 is 1. [2] Let y = 1/x; x*log(x)= -log(y)/y and the limit of log(y)/y for y-> +inf is 0. -- http://mail.python.org/mailman/listinfo/python-list
