Re: zero to the power zero
Paul Connolly wrote:
Hi
Until Monday morning I thought that x^0=1 for all x where x is a finite real
(the notation ^ means "to the power of")
i'd always reasoned it this way...
x^0 = x^(k-k) = x^k/x^k = 1
but my boss (who has a maths degree from Oxford) pointed out to me that the
expression
x^k/x^k doesn't make any sense when x=0 because of division by zero.
I thought about lim x->0 x^k/x^k = 1 so i can see that as x approaches zero
x^k/x^k =1 but I'm not entirely sure that when x gets to zero that it is
reasonable to assume that x^k/x^k = 1 - after all I have no proof that the
graph is continuous at zero
So I'd like to ask
is it provable that 0^0 = 1?
or is it taken as an axiom that 0^0 = 1?
or is there another possibility? (I think that covers all the cases :-)
It depends on what you want to do with it. If you prefer the mapping
x -> x^r with fixed r to be continuous at x=0, then define 0^0 := 1.
But if you would like the mapping x -> x^r with fixed x to be continuous
at r=0, then define 0^0 := 0. For each of these definitions you can find
applications where it is more comfortable to use than the other.
Markus
.
Relevant Pages
- Re: Power Analysis and Multiple Regression and Indifference
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(microsoft.public.win32.programmer.kernel) - Re: Imagine i , j, (-1)^-2
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... On restart, the file testfile.txt exists but is zero bytes long because ... So our so-called safe write to disk, ... We can then happily cut the power, confident that the data will have been ...
(microsoft.public.win32.programmer.kernel) - Re: [PATCH] Add "is_power_of_2" checking to log2.h.
... zero is *not* considered to be a power of two. ... if you peruse the current kernel code, you'll find some tests of the ... so if the powerpc people are ok with that, then the patch itself ...
(Linux-Kernel) |
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