Variations on implication
Michael Hudson
mwh at python.net
Thu Feb 13 13:51:14 CET 2003
Lulu of the Lotus-Eaters <mertz at gnosis.cx> writes:
> |> Paul Rubin wrote:
> |> > => is the traditional mathematical symbol for boolean implication.
> |> > -> looks more to me like some kind of pointer operation. But either
> |> > one is ok with me for this.
>
> Michael Hudson <mwh at python.net> wrote previously:
> |In which context? In my world, => is implication. It's even
> |$\implies$ in LaTeX, I think. -> is often used to denote a map.
>
> FWIW, my math background is primarily in logic, model theory, and set
> theory.
You silly man, you :-)
My area is (more-or-less) algebraic geometry. When I have to worry
about my set theory I know I've strayed into the wrong territory
<wink>.
> In those contexts, there is often a convention of using the single
> line "->" for syntactic implication, i.e. predicate logic. The
> double line "=>" is reserved for semantic implication. So you might
> write (in a simple case):
>
> A -> B
> B -> C
> =>
> A -> C
>
> Or: given the predicates "A implies B" and "B implies C", you are
> authorized to derive the predicate "A implies C" (syllogism).
Ah, fair enough. Learn something every day & all that. I still think
Erik claiming "the traditional symbol for implication is an arrow with
only one horizonal line" is a bit strong.
Cheers,
M.
--
Some people say that a monkey would bang out the complete works
of Shakespeare on a typewriter give an unlimited amount of time.
In the meantime, what they would probably produce is a valid
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