Dan Christensen wrote: > On Wednesday, September 18, 2013 7:11:53 PM UTC-4, Rotwang wrote:
>> >> will follow from people defining exponentiation in the usual way? > > Whatever consequences may arise from a calculation that results in a > value of 1 when it should be 0. The result could be catastrophic.
When "should" 0^0 = 0?
This is what has happened. You were writing a computer program and you wrongly believed that exp(0,0)--or whatever the notation is--would return 0. It didn't, it returned--quite properly--1. Your program being buggy is not a catastrophe. The thing to do with bugs is to fix them[*], _not_ try to "fix" mathematics.
> The most well known theorem that makes use of 0^0 is probably the > Binomial Theorem. And it can easily be restated to avoid its use, > e.g. by stating at the outset that (x+0)^n = x^n, etc.
That (x+0)^n = x^n follows from the definition of addition. Note, btw, that the definition of + begins by saying what x+0 is, it doesn't start with x+1 or x+2.
[* Here's the fix for you. Write a function dansexp(x,y) which when x and y are not both 0 returns exp(x,y); and when x = y = 0 returns 0.]
-- Sorrow in all lands, and grievous omens. Great anger in the dragon of the hills, And silent now the earth's green oracles That will not speak again of innocence. David Sutton -- Geomancies