Function notion

In math, the most general function form is denoted by f(x) = y. This could be considered a named function form since f represents the functions name.

Math also has a notation for anonymous functions, often called mapping instead, of the form x ⟼ y.

Also, math recognizes a piece-wise form for function definition, often used for defining recursive functions that have to deal with several (at least two) cases.

       ⎧ 1                        if n = 1
F(n) = ⎨ 1                        if n = 2
       ⎩ F(n-1) + F(n-2)          if n > 2

Math doesn't really have a defined notation for function application. A function defined as f(x) = 10 - x may be called as f(5) = 10 - 5 = 5, but any more complicated function call will look strange (if correct), especially the calls of curryied functions, e.g. f(5)(8). Probably something unseen in math is a (completely legitimate) form for defining an anonymous function and immediately applying it to some args, e.g. (x ⟼ y ⟼ x + y)(5)(8).