RE: 0^0 = ?

[John W. Eaton]

On 13-Nov-2003, address@hidden <address@hidden> wrote:

| I know that by L'Htpital's Rule you should get:
| 
| ln(y)=x*ln(x) = ln(x)/(1/x)  so
| 
| Lim x->0+  ln(x)/(1/x) = ( 1/x )/( -1/( x^2)) =  
| 
| Lim x->0+ (-x) = 0
| so  ln(y) = 0 and then y=1. 
| 
| Maybe this is the reason for the behavior?

The 0^0 == 1 behavior is part of the IEEE 754 standard for floating
point arithmetic.  The paper "What every computer scientist should
know about floating point arithmetic" by David Goldberg provides a
rationale for the behavior that is a bit different than above (it's at
the end of a section titled "ambiguity").  To start with, I think you
need to look at this as y^x, not x^x.  A quick google search should
turn up a copy of the paper if you want the details.

jwe



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