Free magma

Free magma

A free magma${\displaystyle M_{X}}$ on a set ${\displaystyle X}$ is the "most general possible" magma generated by ${\displaystyle X}$ (i.e., there are no relations or axioms imposed on the generators; see free object). The binary operation on ${\displaystyle M_{X}}$ is formed by wrapping each of the two operands in parentheses and juxtaposing them in the same order. For example