Variations on implication

Michael Hudson mwh at
Thu Feb 13 13:51:14 CET 2003

Lulu of the Lotus-Eaters <mertz at> 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> 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

> 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.


  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
  sendmail configuration file.                    -- Nicholas Petreley

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