[OFFTOPIC] Maps and functions (was Re: Apply a function to each list member?)

[Michael Hudson]

Robin Becker <robin at jessikat.demon.co.uk> writes:

> In article <14370.53219.667492.946075 at gargle.gargle.HOWL>, Charles G
> Waldman <cgw at fnal.gov> writes
[snip]
> >Hmm... what kind of "map" are you thinking of that could send 2 to
> >"both 3 and 4"?  I think such a thing is not a mapping, at least not
> >according to any definition of "map" that I've ever seen.  If you
> >look, for instance, in any basic topology text, you will see that
> >"map" and "function" mean exactly the same thing, when used as nouns.
> >"Map" also has a sense as a transitive verb, which means "to apply a
> >function to", which is where the Python/functional programming usage
> >comes from.
> >
> >
> >
> I define f as a thing which takes integer arguments and outputs sets of
> integers
> 
> presumably I can have such an f that
> 
>         f(2)={3,4}
> 
> to my simple engineer's eyes f could belong to the functions mapping Z--
> >2^Z
> 
> I assume we're not talking that way if the f above isn't a function.

f is a function, as you say from Z to 2^Z. A difference between that
and a function from Z to Z, is that this f throws away a lot of the
algebraic structure of Z (i.e. being a uniquely generated commutative
ring), and so is in many ways less interesting than a function that
preserves this structure.

Regards,
Michael