Talk:Function application

Relation application

Application can be of relations in general; function application is a special case for when the relation is functional. Can something be mentioned about this? I don't know whether anyone has used the term ‘relation application’ in literature. See also: relation composition. —James Haigh (talk) 2015-09-08T04:24:17Z

Function vs Function symbol

@Jochen Burghardt, you're right, I should have been clearer, but I do believe "function symbol" is right. It is not that X is the domain of f, but rather, X is the domain set we are about to assign to f.

And we really do mean "symbol", not the function itself. For example, { (0,0), (1,1), (2,2) } is a function, but we wouldn't use this in that axiom. – Farkle Griffen (talk) 22:52, 13 January 2025 (UTC)[reply]

It might be better to separate the function from the symbol.

Maybe "Given some relation R such that R is a function with a domain X and codomain Y, and a function symbol 'f' ..." – Farkle Griffen (talk) 22:57, 13 January 2025 (UTC)[reply]

I agree that one wouldn't write e.g. { (0,0), (1,1), (2,2) }(x) to denote a function application, so "symbol" seems indeed to be important.

On the other hand, the axiom schema (btw: which one exactly do you mean? Zermelo–Fraenkel_set_theory#Axiom_schema_of_replacement?) should apply to all functions, independently of whether they have got a name or not, so "symbol" there is inappropriate, imo.

In your above answer, I didn't understand why you introduced a relation symbol R (which was never used before in Function_application#Set_theory). What about Given any symbol f denoting a function with a given domain X and codomain Y, ...? - Jochen Burghardt (talk) 20:04, 14 January 2025 (UTC)[reply]