Binary Operations Introduction

Definition: A binary operation * on a set S is a function mapping S x S into S.

To check if a mapping is a binary operation on S, check:
1. any element (a,b) in S x S gets mapped to only one element.
2. any element (a,b) in S x S gets mapped to an element in S.

Example 1: addition on the set of integers is a binary operation.
Example 2: division on the set of integers is NOT a binary operation.
Example 3: division on the set of rationals is NOT a binary operation.
Example 4: division on the set of non-zero rationals is a binary operation.

[MrShostoper]

You don’t know how confused I was until I watched your video, thank you!

[LGgos]

Such a good video, thank you for making it.

[happyboyk]

this definitely helped me out, thanks!