Re: Types of numerals

On Tue, 17 Jan 2006 tomhchappell wrote:

[snip]
> > > XOR is commutative and associative -- it should present no
> > > problems generalizing to any finite positive number of
> > > arguments.
> >
> > Actually, I think that the usage of English
> > "either... or" corresponds more often to
> > XOR than OR.    Generalizing XOR to
> > more than two arguments would be
> > "either ... or .... or ....", i.e. "exactly one of
> > a, b, c, ... or z".
>
> Actually, if it were really XOR being so generalized, it would mean:
> "exactly an odd number of the following arguments" (as opposed
> to "exactly an even number of the following arguments").
However did you arrive at _that_ conclusion?  8-0


> So, "a XOR b" means either a or b but not both;
> "a XOR b XOR c" means either (a and not b and not c) or (b and not a
> and not c) or (c and not a and not b) or (a and b and c).
> "a XOR b XOR c XOR d XOR e" means "Either exactly one of, or exactly
> three of, or all five of, {a, b, c, d, e}".
>
> And so on.
Regards,
Yahya

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