A unit is a measurement of a quantity that is defined or adopted by tradition or law. Other quantities can be expressed as a multiple of the unit. In human history, various unit systems were developed and used in different regions and cultures.
An element 𝑒 of 𝑆 such that 𝑒𝑥 = 𝑥 = 𝑥𝑒 for all 𝑥 ∈ 𝑆 is called a unit element. (When the law of composition is written additively, the unit element is denoted by 0, and is called a zero element.)