# `∞` — Infinity

Literal. Keys: `Alt-8`

`∞` and `¯∞` are approximate real infinities.

``` bpl
∞+3                ⍝ ∞
3÷∞                ⍝ 0
⌊/⍬                ⍝ ∞
⌈/⍬                ⍝ ¯∞
```

`¯∞` \< every finite real \< `∞`. Each infinity equals itself. Empty
min/max identities are infinite even for exact arrays. As IEEE 754
defines, an undefined result with an infinity is NaN:

``` bpl
∞-∞                ⍝ $n
0×∞                ⍝ $n
```

[Infinities and NaN](../numbers.qmd#infinities-and-nan) covers how
infinities combine with exact numbers.

## Errors

- `DOMAIN`: an infinite index or count