NetNews Usenet Archive 1992 #30/NN_1992_30.iso/spool/sci/math/16772

Text File | 1992-12-12 | 1.6 KB | 37 lines

Newsgroups: sci.math
Path: sparky!uunet!zaphod.mps.ohio-state.edu!sdd.hp.com!spool.mu.edu!news.nd.edu!mentor.cc.purdue.edu!seaman.cc.purdue.edu!ags
From: [e-mail] (Dave Seaman)
Subject: Re: Function Terminology
Message-ID: <[e-mail]>
Sender: [e-mail] (USENET News)
Organization: Purdue University
References: <[e-mail]> <[e-mail]> <[e-mail]>
Date: Sat, 12 Dec 1992 18:09:48 GMT
Lines: 25

In article <[e-mail]> [e-mail] (Herman Rubin) writes:
>>In article <[e-mail]> [e-mail] (David G Radcliffe) writes:
>>>Suppose I have a function f: A --> B, and C is a subset of B which
>>>contains the image set of f.  I define a function g: A --> C by
>>>setting g(a) = f(a) for all a in A.  Usually, f and g can be considered
>>>as the same function, but sometimes the distinction is important.

>The function is exactly the same.  A function, in whatever foundational
>system is used, is something which takes arguments in a domain and
>operates on them.  The image set depends only on f and A.  Which
>superset of the range is used does not affect the function.

The point is that that *sometimes* the distinction is important. A definition
that I have seen more than once is:

    A function f is a triple (A,B,GAMMA), where

        1. A is a set, called the domain of f,
        2. B is a set, called the range of f, and
        3. GAMMA is a subset of AxB, called the graph of f,
           with the property ... (you know the rest).

--
Dave Seaman
[e-mail]