> Sorry, if I did not post right. I was not about to cause any

> inconvenience.

>

> I did not say Jack's definition is not possible. I think is not the

> definition mostly used, as usally division by zero is not defined. As

> well as 0^0, if I remember right. Jack's definition leads to an

> agreeable result, I admit.

It depends on the area people work in. For a combinatorian, the equality

0^0 = 1 can work perfectly well; as the left-hand-side denotes the number

of functions from empty set to empty set [*]. Moreover, things like

binomial theorem also work nice with this extension; it allows you to

evaluate the sum [k=0,n,(-1)^k*(n choose k)] as being equal to (1-1)^n, or

simply 0^n (ok, I admit, this is just a contrived academic example).

Likewise, if you work in the area of foundations of mathematics, defining

divisibility using the operation of division is a bit more complicated

than using the straight existential-quantifer with multiplication (just

like Jack did); for the division is only a derived operation in e.g. Peano

Arithmetics and one needs to prove its well-definedness (and possibly some

other properties) first.

On the other hand, an analyst would probably bop you over the head

if he saw 0^0 :-)

Peter

[*] This works even in the much more general framework of set-theory --

If A and B are sets with cardinalities |A| resp. |B|, |A|^|B| is defined

to be the cardinality of the set A^B which is the set of all functions

from B to A. If the sets A and B are finite, the cardinal exponentation

agrees with the usual exponentation of natural numbers.

--

[Name] Peter Kosinar [Quote] 2B | ~2B = exp(i*PI) [ICQ] 134813278