# Algebra : Properties of Real (ℝ) Numbers

## Commutative

Configurable order of numbers:

```
x+y = y+x
xy = yx
```

## Associative

Order that multiplication is applied :

```
(x+y)+z =x+(y+z)
(xy)z = x(yz)
```

## Identity

```
x+0 = x
0+x = x
x.1 = x
1.x = x
```

## Distributive

```
(x + y)z = xz+xy
```

## Inverse

```
x+(-x) = 0
-x + x = 0
1/x . x = 1
x . 1/x =1
```

## Multiplication Property of Zero

```
x.0 = 0
0.x = 0
```

Math

]