| Symbol | Definition |
|---|---|
| ℕ | The set of natural numbers |
| ℤ | The set of integers |
| ∅ | The empty set |
| ∈ | Is an element of |
| ∋ | Such that |
| ∀ | For all |
| ∃ | There exists |
| ∃! | There exists a unique |
| ⊆ | Subset of |
| i:X'⊆X | i is the function that maps elements of X' to elements of its superset X |
| im(f) | In the image of: Given f: X->Y, im(f) is the set of all Ys that can be given by f |
| g∘f | Function f composed with function g |
| HomSet(X, Y) | The set of functions that map X -> Y |
| ⥲ | Isomorphs |
| ≅ | Is an isomorphism of |
| Word | Definition |
|---|---|
| Isomorphic | A -> B and B -> A |
| Commutative set | There exist multiple ways to map from A to B |