>>118
>>122
Trying this again:

Let \math{A} and \math{B} be two sets having nonempty intersection. Then \math{A / B} is \math{A} without the elements in \math{B}. More specifically, \math{(A / B) \cap B = {\emptyset}}. If we think of the slash operator as sending \math{B} to nothing, then the group-theoretic analogue is replacing "nothing" with the identity. Therefore for a group \math{G} and its subgroup \math{N}, the construction \math{G / N} is essentially the group arising from setting all of the elements of \math{N} equal to the identity. This is always a group iff \math{N} is normal.

>why should i care
Quotients are essential tools for investigating algebraic structures. If you want to understand algebra, master this. Once you do you get the First Isomorphism Theorem which is used in countless proofs.