# Category:Numbers

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This category contains results about Numbers.

Definitions specific to this category can be found in Definitions/Numbers.

There are five main classes of number:

- $(1): \quad$ The natural numbers: $\N = \set {0, 1, 2, 3, \ldots}$
- $(2): \quad$ The integers: $\Z = \set {\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots}$
- $(3): \quad$ The rational numbers: $\Q = \set {p / q: p, q \in \Z, q \ne 0}$
- $(4): \quad$ The real numbers: $\R = \set {x: x = \sequence {s_n} }$ where $\sequence {s_n}$ is a Cauchy sequence in $\Q$
- $(5): \quad$ The complex numbers: $\C = \set {a + i b: a, b \in \R, i^2 = -1}$

## Subcategories

This category has the following 25 subcategories, out of 25 total.

### A

### C

### D

### E

### G

### I

### M

### N

### O

### P

### Q

### R

### S

### T

### Z

## Pages in category "Numbers"

The following 35 pages are in this category, out of 35 total.

### A

- Addition on Numbers has no Zero Element
- Arithmetic Addition is Associative
- Arithmetic Addition is Commutative
- Arithmetic Multiplication is Associative
- Arithmetic Multiplication is Commutative
- Associative Law of Addition
- Associative Law of Multiplication
- Associative Law of Multiplication/Euclid's Proof