On Wednesday 03 December 2008 18:48, Stephen C. Gilardi wrote:
> On Dec 3, 2008, at 9:39 PM, Randall R Schulz wrote:
> > OK, so it's consistent with the null-ary (and) (no argument is
> > false) and (or) (there is a true argument). But from that
> > perspective, shouldn't the definition extend to the null-ary case,
> > too?
>
> I think not. How would you decide the values of (=) and (not=)?
> Presumably one should be true and one should be false.
>
> You can also look at (and) and (or) and (+) and (*) as each returning
> the identity element for their operation. There is no such identity
> element for =. That may put it in the same boat as (-) and (/) which
> really require at least one argument to make some sense.

OK. I'll buy that

But it is also the case that subtraction and division _do_ have identity 
elements. They follow directly from the application of the inverse 
operation to the corresponding operator's identity element. In other 
words, the identity element for division is the multiplicative inverse 
of the identity element for multiplication. Likewise for subtraction / 
addition.


> --Steve


Randall Schulz

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