Re: ~ Sets of functions 1

From: Dave Seaman (dseaman_at_no.such.host)
Date: 07/19/04 

Date: Mon, 19 Jul 2004 17:15:46 +0000 (UTC)

On Mon, 19 Jul 2004 16:54:10 +0200, Julien Santini wrote:
>> If that's the definition of "function" then of course you're
>> right. But that's not the definition of "function" that I
>> learned as a child - the definition I learned, and the only
>> one I ever recall seeing, was that a function from X to Y
>> is a subset f of X x Y such that for every x in X there is
>> exactly one y in Y with (x, y) in f. By that definition
>> the statement _is_ literally correct.
>>

> Ok, I guess that must be another bourbakism (lol). The only definition I had
> seen till now was the one I gave.

If we are voting, then I have seen both definitions. The (X,Y,G)
definition has the advantage of being correct from the viewpoint of
category theory, which requires that Mor(A,B) be disjoint from Mor(C,D)
unless A = C and B = D.

Even without categories, I wonder how you can decide whether a given
function is surjective or not, if the codomain of the function is not a
part of its definition. 

-- 
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>