Definition:Addition

Definition
Addition is the basic operation $+$ everyone is familiar with.

For example:


 * $2 + 3 = 5$
 * $47 \cdotp 3 + 191\cdotp 4 = 238 \cdotp 7$

Natural Numbers
Let $\N$ be the natural numbers.

When $\N$ is constructed as a Peano structure $\struct {P, 0, s}$, the addition operation $+$ can be defined as:

Terminology
The symbol $+$ is known as the plus sign.

Hence:
 * $3 + 5$

is usually read:
 * $3$ plus $5$

Commutativity and Associativity
Let $\mathbb F$ be one of the standard number sets: $\N, \Z, \Q, \R$ and $\C$.

Also see

 * Identity Element of Addition on Numbers
 * Inverse Elements for Addition on Numbers


 * Definition:Quaternion Addition