📕 subnode [[@ryan/20210117143856 function]] in 📚 node [[20210117143856-function]]
📓 garden/ryan/20210117143856-function.org by @ryan

A function is a special type of relation

A relation is a function if it satisfies the two following conditions:

  1. $\forall x \in X \exists y \in Y : \langle x,y \rangle \in R$

    • every element of the source X gets mapped by f to some element of the target Y

  2. $\exists \langle x_1,y_1 \rangle, \langle x_2,y_2 \rangle \in R$ holds: $x_1 x_2 \Rightarrow y_1 y_2$

Like categories and subsequently relations, functions can also be composed.

📖 stoas
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