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Metric Space**

A metric space \((X,d)\) consists of a set \(X\) (the 'space') with a function \(d:X\times X\to \mathbb{R}_{\geq0}\) (the 'metric') such that: \(d\) is symmetric, \(\forall x,y\in X:d(x,y)=d(y,x)\), non-degenerate \(\forall x,y\in X:d(x,y)=0\Leftrightarrow x=y\), and obeys the triangle inequality: \(\forall x,y,z\in X:d(x,y)+d(y,z)\geq d(x,z)\).