# Category:Natural Number Addition

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This category contains results about **Natural Number Addition**.

Definitions specific to this category can be found in **Definitions/Natural Number Addition**.

Let $\struct {P, 0, s}$ be a Peano structure.

The binary operation $+$ is defined on $P$ as follows:

$\quad \forall m, n \in P: \begin{cases} m + 0 & = m \\ m + \map s n & = \map s {m + n} \end{cases}$

This operation is called **addition**.

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Natural Number Addition"

The following 29 pages are in this category, out of 29 total.

### A

### C

### N

- Natural Number Addition Commutativity with Successor
- Natural Number Addition Commutes with Zero
- Natural Number Addition is Associative
- Natural Number Addition is Cancellable
- Natural Number Addition is Cancellable for Ordering
- Natural Number Addition is Closed
- Natural Number Addition is Commutative
- Natural Number Commutes with 1 under Addition
- Natural Number Multiplication Distributes over Addition
- Natural Numbers Bounded Below under Addition form Commutative Semigroup
- Natural Numbers under Addition do not form Group
- Natural Numbers under Addition do not form Group/Corollary
- Natural Numbers under Addition form Commutative Monoid
- Natural Numbers under Addition form Commutative Semigroup
- Natural Numbers under Addition form Inductive but not Strictly Inductive Semigroup
- Non-Zero Natural Numbers under Addition do not form Monoid
- Non-Zero Natural Numbers under Addition form Semigroup