# Numbers

Numbers in RuLA represent numeric values, including both integers and decimal numbers.

## Creating Numbers

Write numbers directly without quotes:

```
42          # Integer
-7          # Negative number
3.14159     # Decimal number
0.5         # Decimal less than 1
```

## Number Operations

### Arithmetic

```
5 + 3           # Addition: 8
10 - 4          # Subtraction: 6
3 * 4           # Multiplication: 12
15 / 3          # Division: 5
17 // 5         # Integer division: 3
17 % 5          # Modulo (remainder): 2
2 ** 3          # Exponentiation: 8
```

### Comparison

```
5 > 3           # Greater than: True
5 >= 5          # Greater than or equal: True
3 < 5           # Less than: True
4 <= 5          # Less than or equal: True
```

### Rounding and Precision

```
ROUND(3.14159)          # Round to nearest integer: 3
ROUND(3.14159, 2)       # Round to 2 decimals: 3.14
FLOOR(3.7)              # Round down: 3
CEIL(3.2)               # Round up: 4
```

### Absolute Value and Sign

```
ABS(-5)                 # Returns 5
SIGN(-5)                # Returns -1
SIGN(5)                 # Returns 1
SIGN(0)                 # Returns 0
```

## Useful Number Functions

| Function                                                                              | Description                  | Example                            |
| ------------------------------------------------------------------------------------- | ---------------------------- | ---------------------------------- |
| [`SUM`](/rule-language/operators/mathematical-operators/sum.md)                       | Sum of all numbers in a list | `SUM([1, 2, 3])` → `6`             |
| [`AVG`](/rule-language/operators/mathematical-operators/avg.md)                       | Average of numbers in a list | `AVG([1, 2, 3])` → `2`             |
| [`MIN`](/rule-language/operators/mathematical-operators/min.md)                       | Smallest number in a list    | `MIN([3, 1, 2])` → `1`             |
| [`MAX`](/rule-language/operators/mathematical-operators/max.md)                       | Largest number in a list     | `MAX([3, 1, 2])` → `3`             |
| [`ROUND`](/rule-language/operators/mathematical-operators/round.md)                   | Round to nearest integer     | `ROUND(2.5)` → `3`                 |
| [`ROUND(number, decimals)`](/rule-language/operators/mathematical-operators/round.md) | Round to N decimal places    | `ROUND(3.14159, 2)` → `3.14`       |
| [`FLOOR`](/rule-language/operators/mathematical-operators/floor.md)                   | Round down to integer        | `FLOOR(3.9)` → `3`                 |
| [`CEIL`](/rule-language/operators/mathematical-operators/ceil.md)                     | Round up to integer          | `CEIL(3.1)` → `4`                  |
| [`ABS`](/rule-language/operators/mathematical-operators/abs.md)                       | Absolute value               | `ABS(-5)` → `5`                    |
| [`SIGN`](/rule-language/operators/mathematical-operators/sign.md)                     | Sign of number (-1, 0, 1)    | `SIGN(-5)` → `-1`                  |
| [`SQRT`](/rule-language/operators/mathematical-operators/sqrt.md)                     | Square root                  | `SQRT(16)` → `4`                   |
| [`CLAMP`](/rule-language/operators/mathematical-operators/clamp.md)                   | Constrain to range           | `CLAMP(10, 0, 5)` → `5`            |
| [`COMB`](/rule-language/operators/mathematical-operators/comb.md)                     | Combinations (n choose k)    | `COMB(5, 2)` → `10`                |
| [`SUM_PRODUCT`](/rule-language/operators/mathematical-operators/sum_product.md)       | Sum of products              | `SUM_PRODUCT([1,2], [3,4])` → `11` |

## Working with Lists of Numbers

Aggregate functions work on lists:

```
numbers = [10, 20, 30, 40]
SUM(numbers)        # 100
AVG(numbers)        # 25
MIN(numbers)        # 10
MAX(numbers)        # 40
```

## Type Checking

To check if a value is a number:

```
# Numbers are always known (not None/unknown)
known(42)           # True
unknown(42)         # False
```


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