Addition

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Addition is the binary mathematical operation of putting numbers or quantities together (adding). The plus sign "+" means that objects are added up. The numbers that being added are called "addends" and the result is called "sum".

Properties

Commutativity

Addition is commutative, meaning a + b = b + a.

Associativity

Addition is associative, meaning a + (b + c) = (a + b) + c

Zero and one

Adding 0 to a number is not changing the number: a + 0 = 0 + a = a. For any integer a, (a + 1) means least integer greater than a, also known as successor of a.

Sum

If S is a finite set of numbers, then all its elements can be added together using sigma notation.

Addition of natural and real numbers

Natural numbers

Integers

Rational numbers (fractions)

Two fractions can be added up using this formula: . However it is easier to use least common denominator.

Real numbers