[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
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