4 ms·
> A function is a relationship between two sets Ok then what is relationship? There's a whole theory of relations, and I'd rather not dive into that for the ar
by deepsun 3y ago
> A function is a relationship between two sets
Ok then what is relationship? There's a whole theory of relations, and I'd rather not dive into that for the article. Also, drawing arrows can give misleading intuition.
It's better to define a function as a set of pairs, then you don't need to use anything else not introduced yet.
- smohare 3y ago[dead]
- JadeNB 3y ago> It's better to define a function as a set of pairs, then you don't need to use anything else not introduced yet. If you're looking towards category theory, it may arguably be better to think in terms of abstract arrows as much as possible, so as not to get confused by non-"concrete" categories where there's no obvious "function semantics" for morphisms.
- SantalBlush 3y agoIs there a simple example you could use to illustrate the point? This is interesting.
- ginnungagap 3y agoLet (X,≤) be a partially ordered set. Define a category C whose objects are the elements of X, while for the morphisms there is a single arrow x→y iff x≤y. Those are called posetal categories and are often used as examples
- boris_m 3y agoRelevant chapter from the book: https://abuseofnotation.github.io/category-theory-illustrated/04_order/ https://abuseofnotation.github.io/category-theory-illustrate...
- SantalBlush 3y agoThat makes perfect sense and is very helpful. Thank you.
- smadge 3y agoA relationship between two sets is a set of pairs.