 A pointed set is an algebra with one constant, say \(c\). The free pointed set on \(x\) and \(y\) has three elements, \(x, y\), and \(c\). A bipointed set is an algebra with two constants \(c\) and \(d\), and the free bipointed set on \(x\) and \(y\) then has four elements, \(x, y, c\), and \(d\).