# Python Numbers Module

The `numbers` module defines a hierarchy of numeric abstract base classes (ABCs) which progressively define more operations. It is useful for checking if an object acts like a number, rather than checking for a specific type (like `int` or `float`).

## Importing the Module

```python
import numbers
```

## The Numeric Hierarchy

The module defines the following hierarchy of ABCs:

1.  **`Number`**: The root of the numeric hierarchy.
2.  **`Complex`**: Subclass of `Number`. Describes complex numbers and includes operations that work on the complex plane.
3.  **`Real`**: Subclass of `Complex`. Describes real numbers (like `float`).
4.  **`Rational`**: Subclass of `Real`. Describes rational numbers (like `fractions.Fraction`).
5.  **`Integral`**: Subclass of `Rational`. Describes integral numbers (like `int`).

## Type Checking

The primary use case for this module is to check if a number belongs to a certain category using `isinstance()`.

### Checking for Integers

If you want to accept any integer-like number (including `int` and potentially other custom integer types), check against `numbers.Integral`.

```python
import numbers

x = 10
print(isinstance(x, numbers.Integral)) # Output: True

y = 10.5
print(isinstance(y, numbers.Integral)) # Output: False
```

### Checking for Real Numbers

If you want to accept floating-point numbers or integers (since integers are mathematically real numbers), check against `numbers.Real`.

```python
import numbers

x = 10.5
print(isinstance(x, numbers.Real)) # Output: True

y = 10
print(isinstance(y, numbers.Real)) # Output: True
```

### Checking for Complex Numbers

`numbers.Complex` covers complex numbers, real numbers, and integers.

```python
import numbers

z = 3 + 4j
print(isinstance(z, numbers.Complex)) # Output: True
```

## Note on `decimal.Decimal`

It is important to note that `decimal.Decimal` does **not** inherit from `numbers.Real`. This is because `Decimal` implements decimal floating-point arithmetic, which behaves differently from binary floating-point arithmetic (represented by `float` and `numbers.Real`). `Decimal` inherits from `numbers.Number`.

[[programming/python/python]]