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diff --git a/doc/arithmetic.md b/doc/arithmetic.md index 3fa9ab9a..ee93b984 100644 --- a/doc/arithmetic.md +++ b/doc/arithmetic.md @@ -138,6 +138,33 @@ Modulus (`|`) is similar to the modular division operation written `%` in C-like Unlike in APL, a left argument of 0 fails or returns a not-a-number result. Set `𝕨` to `∞` to keep `𝕩` intact, but do note that if `𝕩<0` this will return `∞`. +## Comparisons + +BQN uses the six standard comparison functions of mathematics. For each pair of atoms the result is 1 if the comparison is true and 0 if it's false. These functions do the obvious thing with numeric arguments, but are extended to other types as well. + +| Name | Glyph | < | = | > | Domain +|--------------------------|:-----:|---|---|---|------- +| Equals | `=` | 0 | 1 | 0 | Any +| Not Equals | `≠` | 1 | 0 | 1 | Any +| Less Than or Equal to | `≤` | 1 | 1 | 0 | Data +| Less Than | `<` | 1 | 0 | 0 | Data +| Greater Than | `>` | 0 | 0 | 1 | Data +| Greater Than or Equal to | `≥` | 0 | 1 | 1 | Data + +The *ordered* comparisons `≤<>≥` are defined on numbers and characters (and arrays, by pervasion); they give an error for operation or namespace arguments. They order numbers as you'd expect, and characters by their code points. A character is considered greater than any number, even if it's `∞`. + + 3‿4‿5‿6 ≤ 5 + + 'c' < "acbz" + + ¯∞‿π‿∞ ≥ @‿'0'‿'?' + +Equals and Not Equals are the two *equality* comparisons. Equals tests for [atomic equality](match.md#atomic-equality) between each pair of atoms, as described in the Match documentation. Essentially, it returns `1` only if the two values are indistinguishable to BQN and `0` otherwise. Values of different types can never be equal, and characters are equal when they have the same code point. + + +‿-‿×‿÷ = ⊑⟨-⟩ + + 'b' ≠ "abacba" + ## Pervasion Arithmetic primitives act as though they are given [depth](depth.md#the-depth-modifier) 0, so that with array arguments they treat each atom independently. While the examples above use only numbers or lists of them, arithmetic applies to nested and high-rank arrays just as easily. |