Re: Types of numerals
| From: | tomhchappell <tomhchappell@...> |
|---|
| Date: | Tuesday, January 17, 2006, 19:34 |
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--- In conlang@yahoogroups.com, Jim Henry <jimhenry1973@G...> wrote:
>
> On 1/17/06, tomhchappell <tomhchappell@y...> wrote:
> > --- In conlang@yahoogroups.com, John Vertical <johnvertical@H...>
> > > wrote:
>
> > How are "either" and "neither" similar to "both"?
> >
> > > These seem to be related to the logical
> > > connectivities AND, NOR and OR.
> >
> > Oh, I get it.
> > both --- and
> > either --- or
> > neither --- nor
> >
> > > NAND and XOR would be easy additions to this
> > > family, were they not tricky to generalize for
> > > more than 2 arguments.
> >
> > 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").
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.
> Generalizing OR to
> three or more arguments would require
> something like "one or more or all of
> a, b, c, ... or z".
Yes; but AND and OR are commutative and associative, just like XOR;
so they generalize easily to any finite positive number of arguments.
Tom H.C. in MI
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