Question

Would you argue that all mathematical constructs are functions? including numbers?

Answer 1

not really, a function needs an input and an output

Answer 2

Change functions to sets and you have something.

Answer 3

Yeah, I agree!
@zzr0ck3r isn't a function a connection between sets? Like if you have a pair (x,y) this represents the ouput of some function y = f(x). but there also is some mapping that maps x to y, namely f.

Answer 4

The simplest definition is: a function is a bunch of ordered pairs of things (in our case the things will be numbers, but they can be otherwise), with the property that the first members of the pairs are all different from one another.

Thus, here is an example of a function:

[{1, 1}, {2, 1}, {3, 2}]

This function consists of three pairs, whose first members are 1, 2 and 3.
It is customary to give functions names, like f, g or h, and if we call this function f, we generally use the following notation to describe it:

f(1) = 1, f(2) = 1, f(3) = 2

Answer 5

Yes, @LannyXX . But that is just saying, that all functions are sets, but the other way around is not true.

Even the number 2 is really a set, because what you really mean when you say 2 is that the symbol 2 is a representative for the equivalence class containing 2.