# Comparison¶

*Comparison operators* can be used to compare two values, to test if
they are equal or to see what order they are in. Comparison operators
always return a boolean value.

Values of almost any type can be compared: numeric types, booleans, characters, strings, and any pair, sum, or container types built out of these. For example, sets of pairs of natural numbers and strings can be compared:

```
Disco> {(3, "hi"), (4, "there"), (6, "world")} < {(10, "what")}
true
```

See the individual pages about each type for more information on how comparison works on values of that type.

Functions, on the other hand, cannot be compared, because in general this would require testing the functions on every single possible input, of which there might be infinitely many.

```
Disco> (\n:N. n) < (\n:N. n+1)
Error: values of type a2 → a3 cannot be compared.
https://disco-lang.readthedocs.io/en/latest/reference/not-qual.html
```

The

`==`

operator is for testing equality. For example,Disco> 3 == 5 false Disco> "hi" == "hi" true

Equality is one critical point where Disco syntax has to deviate from standard mathematical notation: be sure to keep in mind the difference between

`=`

(which is used to define things) and`==`

, used for testing whether two things are equal. For more information on the difference, see the page on definition vs equality testing.The

`/=`

operator (also written`≠`

or`!=`

) means “not equal to”. It is true if and only if its two arguments are not equal. The syntax`/=`

is supposed to remind us of the standard mathematical notation of an equality sign with a slash through it (`≠`

). However,`!=`

is also provided for those used to this operator in other programming languages.There are four operators that can be used to test the ordering of two values:

`<`

tests whether the first value is less than the second.`>`

tests whether the first value is greater than the second.`<=`

, also written`≤`

or`=<`

, tests whether the first value is less than or equal to the second.`>=`

, also written`≥`

or`=>`

, tests whether the first value is greater than or equal to the second.

You can chain multiple comparisons; this always means the same thing as combining all the individual comparisons with “and”. For example,

`3 <= x < y <= 10`

means the same thing as`3 <= x /\ x < y /\ y <= 10`

.