Re: Searching for a function

• To: mathgroup at smc.vnet.net
• Subject: [mg70850] Re: [mg70813] Searching for a function
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 28 Oct 2006 23:39:41 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200610280921.FAA16103@smc.vnet.net>

```I don't understand your question.  If B is not empty, then there ALWAYS
exists at least one function from A to B:  If A is empty, then the
function with empty graph is a function from A to B; if A is nonempty,
then any constant function with value an element of B is a function from
A to B.

Bonny Banerjee wrote:
> Is it possible for Mathematica to solve this problem:
>
> Given sets A and B, does there exist a function from A to B? If yes, what is
> the function?
>
>
> Here is an example:
>
> Let, A = {x such that 0<x<11 and Mod[x,2]==0}
>
> B = {y such that 0<y<11 and Mod[y+1,2]==0}
>
> Then, there exists a function from A to B
>
> y = x - 1
>
>
> Thus, is there a way to specify arbitrary sets A, B, and use Mathematica to
> figure out whether there exits a function from A to B or not?
>
> Thanks,
> Bonny.
>
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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