# Infinity¶

class `abjad.mathtools.Infinity.``Infinity`

Infinity.

All numbers compare less than infinity:

```>>> 9999999 < Infinity
True
```
```>>> 2**38 < Infinity
True
```

Infinity compares equal to itself:

```>>> Infinity == Infinity
True
```

Negative infinity compares less than infinity:

```>>> NegativeInfinity < Infinity
True
```

Initializes as a system singleton at start-up.

Available as a built-in after Abjad starts.

Attributes Summary

 `__eq__` Is true when `argument` is also infinity. `__float__` Convert infinity to float. `__ge__` Is true for all values of `argument`. `__gt__` Is true for all noninfinite values of `argument`. `__hash__` Hashes infinity. `__le__` Is true when `argument` is infinite. `__lt__` Is true for no values of `argument`. `__sub__` Subtracts `argument` from infinity.

Special methods

`(AbjadValueObject).``__copy__`(*arguments)

`__eq__`(argument)

Is true when `argument` is also infinity.

Returns true or false.

`__float__`()

Convert infinity to float.

Returns float.

`(AbjadObject).``__format__`(format_specification='')

Set `format_specification` to `''` or `'storage'`. Interprets `''` equal to `'storage'`.

Returns string.

`__ge__`(argument)

Is true for all values of `argument`.

Returns true.

`__gt__`(argument)

Is true for all noninfinite values of `argument`.

Returns true or false.

`__hash__`()

Hashes infinity.

Required to be explicitly redefined on Python 3 if __eq__ changes.

Returns integer.

`__le__`(argument)

Is true when `argument` is infinite.

Returns true or false.

`__lt__`(argument)

Is true for no values of `argument`.

Returns true or false.

`(AbjadObject).``__repr__`()

Gets interpreter representation of Abjad object.

Returns string.

`__sub__`(argument)

Subtracts `argument` from infinity.

Returns infinity or 0 if `argument` is also infinity.