basic question on definition of function

Question

on wikipedia it says that a function is a relation or process that associates each x of X an element y of Y. I can understand how a function is a relation defined by some equation but can't really understand the interpretation as a process.

Is it necessary to understand this and if so could someone make this clearer for me, thanks

Answer 1

More precisely by definition given $2$ sets $X$ and $Y$ a function $f:X\to Y$ is a "law" which associates to any value $x\in X$ one and only one value $y\in Y$.

Note that we don't need that $f$ is defined by an explicit formula or expression the definiton indeed works in a more general context.

For example we can consider the function $f$ which associates to any person the mother.

Or in a more mathematical context, we can consider the function $f:\mathbb{N}\to\mathbb{N}$ which associates to any natural number $n$ the corresponding $n^{th}$ prime number.

Refer also to the related

• What exactly is a function?

• Why is $\sin : \mathbb{R} \to [-5,5] $ different from $\sin : \mathbb{R} \to \mathbb{R}$?