special
some functions in set theory have special status
| name | domain | codomain | input | output | description |
|---|---|---|---|---|---|
| id | ξ | ξ | x | x | the identity function, that returns whatever is given to it |
| eq | ξ×ξ | 𝔹 | a, b | a == b | two objects are mathematically the same |
| is | ξ×ξ | 𝔹 | a, b | a is b | a is the same object as b |
eq and is are comparable to ev, which also checks equality but specifically under a certain ordering.
identity
identity: ξ → ξ x | x | the identity function, that returns whatever is given to it | description: the identity function. it returns whatever is given to it
is
the is function tells you whether a is b. a and b can compare equivalent via [eq] but identify different via [is]
this is important for languages where
yaml