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Re: Searching for a function

• To: mathgroup at smc.vnet.net
• Subject: [mg70878] Re: Searching for a function
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Mon, 30 Oct 2006 05:33:12 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <ehv8vp$g6f$1@smc.vnet.net> <ei1a0t$97b$1@smc.vnet.net>

Bonny Banerjee wrote:
> "Bonny Banerjee" <banerjee.28 at osu.edu> wrote in message 
> news:ehv8vp$g6f$1 at smc.vnet.net...
>> 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.
>>
>>
> 
> 
 > I am looking for continuous functions only from set A to set B. Sorry 
 > for not making it clear.
 >
 > --Bonny.
 >
And polynomial functions -- say, obtained by interpolation as suggested 
by other posters -- are not continuous, aren't they?

Regards,
Jean-Marc