Are functions arbitrary? If so, is that okay?

manpreet Best Answer 2 years ago

I'm learning about functions between sets. I get the concept. But I'm having a hard time drinking the kool-aid, so to speak. There's some part of my mind that thinks (loudly),

Wait. How does this author justify claiming that he can connect two things together however he likes. There has to be some justification to connect them.

But I get that -really- all a function between two sets is doing is saying is

This is what things would look like if you connected the elements of these two sets

But still, intuitively, it strikes me as potentially problematic. For instance, we used to be able to assign any element we wanted to a set - that turned out to be a problem. I don't necessarily wonder whether functions would lead to the same problem, but perhaps to some other problem arising from arbitrarily relating things?

Do functions have the potential to lead to that kind of a problem, or any other problem? Is there a better way to think of them than I've described?

manpreet 2 years ago