[Jprogramming] college math 0^0

[Eugene McDonnell]

On Dec 7, 2005, at 9:19 AM, Robert Cyr wrote:

> My intent was to introduce my college student son to J.
>
> How do I get J to signal an indeterminate value for 0^0 ?
>
> example:
> plot (1 - cos x) ^ tan x =: steps (-pi),(pi), 1000
>
> 1. does not signal the problem.
> 2. does not help in solving :
>       lim(x->0+)(1-cosx)^(tan x)

Donald Knuth in "Two Notes on Notation", AMM 1992, 403-422, on pp.  
407-8 makes the case for 0^0 being 1, as it is in J and APL. He  
writes, in opposition to the view that 0^0 should be undefined,
*****************
But no, no, ten thousand times no! Anybody who wants the binomial  
theorem

     (x+y)^n = Sum from k=0 to n  of   (k!n) * (x^k)*(y^n-k)

to hold for at least one negative integer n must believe that 0^0 =  
1, for we can plug in x = 0 and y = 1 to get 1 on the left and 0^0 on  
the right. The number of mappings from the empty set to the empty set  
is 0^0. It _has_ to be 1.
*****************

But Ken knew that long ago. In "APL Language", which Ken and Adin  
Falkoff and I wrote in 1975,  0^0 is defined to be 1.

Eugene McDonnell