"Intro should be re-written ..."

An algebraic structure is a set equipped with operators that follow certain laws, such as a group, which is a pair $(X, \\bullet)$ where $X$ is a set and $\\bullet$ is an operator that follows certain laws\. Given an algebraic structure, we can simply throw away the operators and recover the set \($X$, in this case\), which is known as the "underlying set" of the structure\.

Intro should be re-written so as not specific to algebraic structures.