The Mathematics Ontology Bible · Version 1.0
Appendix A: Symbol Glossary
| Symbol | Meaning |
|---|---|
| ∀ | For all |
| ∃ | There exists |
| ⟹ | Implies |
| ⟺ | If and only if |
| ¬ | Not |
| ∧ | And |
| ∨ | Or |
| ∈ | Is an element of |
| ∉ | Is not an element of |
| ⊆ | Is a subset of |
| ⊂ | Is a proper subset of |
| ∅ | The empty set |
| ∪ | Union |
| ∩ | Intersection |
| × | Cartesian product |
| 𝒫(A) | Power set of A |
| A | |
| ℕ | Natural numbers {0, 1, 2, …} |
| ℤ | Integers {…, -1, 0, 1, …} |
| ℚ | Rational numbers |
| ℝ | Real numbers |
| ℂ | Complex numbers |
| ℍ | Quaternions |
| ℵ₀ | Countable infinity (cardinality of ℕ) |
| 2^ℵ₀ | Cardinality of ℝ |
| ω | First infinite ordinal |
| π₁(X) | Fundamental group of X |
| Hₙ(X) | n-th homology group of X |
| ⊕ | Direct sum |
| ⊗ | Tensor product |
| Hom(A,B) | Set of morphisms from A to B |
| ∘ | Composition |
| ≅ | Isomorphism |
| ≃ | Homotopy equivalence |
| ∫ | Integral |
| ∑ | Sum |
| ∏ | Product |
| ℒ | Lagrangian |
| ℋ | Hamiltonian |