>>11906164Functions are more interesting practically, so perhaps that practical value spills over into what they can do in mathematics.
Functions roughly describe certainty. If y is f(x) then it it is to the exclusion of f(x) = z. Functions encapsulate more information and enable more powerful reasoning.
Intellectually, the more ideas and propositions you can nail down as functions, the "farther" you can reason about them because you can make more valid conclusions.
I program for a living and I write in functional programming languages. Computer memory can be messy and chaotic, so it can be difficult to know what really happens when your software is running on them. Functional programming enables you to make strong assumptions about the nature of what a computer does, which enables programmers to make fast and reliable code.
