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[parent] Viewing Correction to 'function'
image by Luis Trucco

Correction id: 6571
Filed on: 2005-05-03 20:37:05
Status: Accepted on 2005-06-01 02:19:19
Type: Meta/Minor

Correction text:
Iwould write:
The image of f, denoted f(A), is the subset of B
 {f(a)|a \in A} \subseteq B .
If f(A)=B the function is onto or surjective.
To avoid misslinks I would change the word mean (signify, denote ?);
I think univeral agreement is an oximoron, agreement suffice an avoid a misslink.
 Luis

Comment from object owner djao:
> Iwould write:
> The image of f, denoted f(A), is the subset of B
> {f(a)|a \in A} \subseteq B .

This notation is being rejected for the reasons given in the message post.

> If f(A)=B the function is onto or surjective.

Surjective already has its own entry, and in fact surjective is already listed in the related words section. It does not need to be defined in the main body text.

> To avoid misslinks I would change the word mean (signify, denote ?);

I do not make any attempts to avoid superfluous links. Common words like mean cause mislinks in dozens of places, not just here. The correct solution is to attack the source of the problem, not the dozens of symptoms. File a correction upon the "mean" entry and ask for a lowering of the link priority of "mean".

In this case, denote is a better word anyway, so I will use it.

> I think univeral agreement is an oximoron, agreement suffice an
> avoid a misslink.

An oxymoron is when two adjacent terms contradict each other. Universal agreement is not an oxymoron; at worst you could argue that is redundant, but there is certainly no contradictory meaning.

Redundancy is sometimes good to emphasize a point. Here I feel that the redundancy is worth the mislink. Again, the proper way to correct a mislink is to file a correction on the mislinked term and ask for the mislinked term (in this case, universal) to adjust their link priority. It is way easier to correct the source entry's link priority than to perpetually chase and clean up after all the dozens of mislinks that a common word like "universal" sprouts.
Discussion
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set notation by djao on 2005-05-24 15:02:42
The problem with your notation

{f(a) | a \in A}

is that this construction isn't strictly allowed in formal set theory. Of course, I realize that most planetmath entries, including this one, are far from formal, but at the same time, I believe that the definition of function is close enough to the realm of set theory that one should at least make an effort to stick with constructions which are close to their formal counterparts, even if those constructions are not themselves formal.

A formal specification of a set only allows a simple membership statement on the left side together with an arbitrarily complicated (but finite) expression on the right side. You aren't allowed to use expressions like f(a) on the left side. For higher level definitions it is fairly common to use expressions like f(a) on the left side, but again, my feeling is that function is too low level to allow such usage in its definition.
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