Set-Theory

Binary Relation

Math Set-Theory

A binary relation \(R\) over sets \(X\) and \(Y\) is a subset of the cartesian product of \(X \times Y\). Where \(X\) is the domain, or set of departure of \(R\), and \(Y\) is the codomain, or set of destination of \(R\). An element \(x \in X\) is related to \(y \in Y\), iff the ordered pair \((x, y)\) is found within the (above) subset.

Bijective Function

Math Set-Theory Real-Analysis

A function is bijective or “invertible” if it is Both one-to-one and onto (injective and surjective) In other words: each element of one set is paired with exactly one element of the other set, and vice versa