Chapter 2: functions

[nbloomf]

Small comment about the discussion on functions.

Functions are defined in terms of binary relations, and they have a nice characterization that is dual to the concepts of "one-to-one" and "onto".

A function is a binary relation $f \subseteq A \times B$ that is also

• total, meaning that for every $a \in A$ there exists a $b \in B$ such that $(a,b) \in f$, (compare to onto) and
• well-defined, meaning that if $(a_1,b) \in f$ and $(a_2,b) \in f$ then $a_1 = a_2$ (compare to one-to-one).

[bor0]

This is an interesting observation. However, I am wondering if it should go in the footnotes, as it may be distracting a bit.