Mathematical logic and foundations Theorem

Commutativity of addition

Builds on Addition of natural numbers Mathematical induction

Statement

For all natural numbers $a$ and $b$ , $a + b = b + a$ . Here $+$ is the addition of natural numbers.

Remarks

The proof from the recursive definition of addition uses the principle of mathematical induction two times. An operation $\ast$ on a set is commutative when $x \ast y = y \ast x$ for all $x$ and $y$ . Multiplication of natural numbers is also commutative. Subtraction of integers is not commutative: $3 - 1 \neq 1 - 3$ .

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To understand this page from the ground up, read these 7 pages in order. The foundations come first.

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Tag	`0DFZNHJ0S2`
URI	`m2://0DFZNHJ0S2`
Kind	statement, theorem
Writing	W0 stub
MSC	03F30
Status	This copy of the site has no build data. Run `m2 status 0DFZNHJ0S2`.
Uses	Addition of natural numbers, Mathematical induction

Commutativity of addition

Statement

Remarks

Reading path

Further reading

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