Add comparison functions to arithmetic documentation

3 files changed, 34 insertions, 7 deletions

diff --git a/doc/README.md b/doc/README.md
index ab347e99..9e3f3e3a 100644
--- a/doc/README.md
+++ b/doc/README.md
@@ -28,7 +28,7 @@ Concepts:
 - [Function trains](train.md)
 
 Primitives:
-- [Arithmetic](arithmetic.md) (`+-×÷⋆√⌊⌈|`)
+- [Arithmetic](arithmetic.md) (`+-×÷⋆√⌊⌈|≤<>≥=≠`)
 - [Array depth](depth.md) (`≡` and `⚇`)
 - [Array dimensions](shape.md) (`≢=≠`)
 - [Assert](assert.md) (`!`)
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.
diff --git a/doc/primitive.md b/doc/primitive.md
index 531ffb13..ff40f843 100644
--- a/doc/primitive.md
+++ b/doc/primitive.md
@@ -26,12 +26,12 @@ Functions that have significant differences from APL functions are marked with a
 | `∨`   | [Sort Down](order.md#sort)                          | [Or](logic.md)*
 | `¬`   | [Not](logic.md)*                                    | [Span](logic.md)*
 | `\|`  | [Absolute Value](arithmetic.md#additional-arithmetic)| [Modulus](arithmetic.md#additional-arithmetic)
-| `≤`   |                                                     | [Less Than or Equal to](https://aplwiki.com/wiki/Less_than_or_Equal_to)
-| `<`   | [Enclose](enclose.md)                               | [Less Than](https://aplwiki.com/wiki/Less_than)
-| `>`   | [Merge](couple.md)*                                 | [Greater Than](https://aplwiki.com/wiki/Greater_than)
-| `≥`   |                                                     | [Greater Than or Equal to](https://aplwiki.com/wiki/Greater_than_or_Equal_to)
-| `=`   | [Rank](shape.md)*                                   | [Equals](https://aplwiki.com/wiki/Equal_to)
-| `≠`   | [Length](shape.md)                                  | [Not Equals](https://aplwiki.com/wiki/Not_Equal_to)
+| `≤`   |                                                     | [Less Than or Equal to](arithmetic.md#comparisons)
+| `<`   | [Enclose](enclose.md)                               | [Less Than](arithmetic.md#comparisons)
+| `>`   | [Merge](couple.md)*                                 | [Greater Than](arithmetic.md#comparisons)
+| `≥`   |                                                     | [Greater Than or Equal to](arithmetic.md#comparisons)
+| `=`   | [Rank](shape.md)*                                   | [Equals](arithmetic.md#comparisons)
+| `≠`   | [Length](shape.md)                                  | [Not Equals](arithmetic.md#comparisons)
 | `≡`   | [Depth](depth.md)*                                  | [Match](match.md)
 | `≢`   | [Shape](shape.md)                                   | [Not Match](match.md)
 | `⊣`   | [Identity](identity.md)                             | [Left](identity.md)