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MathGroup Archive 2006

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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>
  • Reply-to: murray at math.umass.edu

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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