| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
on difference between Image and Range of function:
Image, is the set of all possible values that the function can take.
Range is the field that the image is part of.
are these ok definitions?
example exp(*) has image of R+ (looking at domain = R only)
but range of exp(*) is R
/Nasser
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1523.1 | How mathematicians abuse the language | PULPO::BELDIN_R | Pull us together, not apart | Mon Nov 18 1991 09:54 | 28 |
-< difference of image and range of function >-
Let my try to clarify the language.
Suppose it is said that "f maps X into Y".
We usually say that "X is the domain of f" and "Y is the range of f".
We define the image as an associated function,
"I maps P(X) into P(Y)",
f
where P(U) is the power set of U.
Then we call I (X) the "image of X under f".
f
So, your question can be answered as follows:
"I (X) = Y" means the same as "f maps X onto Y".
f ----
What happens is that in different discussions, different background
assumptions are made and therefore different language is used. In abstract
algebra, you learn about dualism which allows you to say the same thing in
(at least) two distinct ways. We are often sloppy about which form of
language we use. That always make it tough.
Dick
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