Re: Types of functions and relations

"A. Boom" <aboom@xxxxxxxxxx> wrote in message
news:1ISdnaNxOs2spu3fRVn-qg@xxxxxxxxxxxxx
> Hi,

[...snip...]

> What is the name of the set whose elements constitute the pairs that the
> function maps to. for instance, let f: A -> B be a function with
> elements of the set F <= AxB. What is the formal name of F?
>
> Thanks in advance, Adam.

You may possibly have a misunderstanding here. A common terminology is:

A is the 'domain' of f
B is the 'codomain' of f (some say 'target' instead of 'codomain')

The function f maps elements of A to elements of B (not to pairs in AxB
as you state). If 'a' is in A and f(a)=b, then 'b' is called the image
of 'a' under f, and 'a' is a pre-image of b. The set of all images of
elements of A under f is a subset of B (possibly all of B) called the
'range of f'.

The subset F you describe above of all pairs (a,b) such that 'a' is
in A, 'b' is in B and f(a)=b is commonly called the 'graph' of f.

Not all books define all these terms in the same way, and this
causes some confusion and misunderstanding.
--
Jim Buddenhagen

.

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