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.