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

Josh Daghlian jcd2 at lehigh.edu
Tue Nov 9 00:58:41 CET 1999

```Here is an example of something that maps a single input to multiple outputs:

y(x) = arcsin(x)
For x = 0, y(0) == ..., -2*pi, -pi, 0, pi, 2*pi, 3*pi, ...

Note that this is *not* a function (in the math sense), but it is a
perfectly good mapping that lots of nerdy folks use all the time.

Now lets move to alt.math or something.  :)
Cheers.
--josh

In article <m3eme59dg1.fsf at atrus.jesus.cam.ac.uk>, Michael Hudson
<mwh21 at cam.ac.uk> wrote:

:  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

<cut>

:  > 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

```