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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

Carlos Bacca
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  • In France there is two related definitions, functions and applications: your definition corresponds to application because the domain of the function is ALL the set X while, for example the real function $f(x)=\dfrac 1x$ is not defined in $x=0$. In other words, many times you are concerned with an expression for which you have to define the domain of it while for your function the domain is given. – Ataulfo Sep 02 '18 at 10:56

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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

user
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