Embedding Theorem/Motivation

Motivation for Embedding Theorem
The following is a frequently occurring circumstance in the field of abstract algebra.


 * We have a magma $\struct {T_1, \circ}$.
 * $\struct {T_1, \circ}$ is isomorphic to another magma $\struct {T_2, *}$.
 * $\struct {T_2, *}$ is embedded in a magma $\struct {S_2, *}$.
 * We want to embed $\struct {T_1, \circ}$ in its own magma $\struct {S_1, \circ}$ such that $\struct {S_1, \circ} \cong \struct {S_2, *}$.

This can always be done, as the Embedding Theorem theorem shows.