#separator:tab #html:false #notetype:Basic #deck:Math::Sets::Symbol index Read the symbol: ∈ ∉ ∋ ∌ is a member of, is not, contains. Explained under: glossary entry: membership. symbol Which symbol says: is a member of, is not, contains? ∈ ∉ ∋ ∌ (explained under: glossary entry: membership) symbol reverse Read the symbol: {a, b, c} the set whose members are a, b, c. Explained under: what is a set. symbol Which symbol says: the set whose members are a, b, c? {a, b, c} (explained under: what is a set) symbol reverse Read the symbol: {x ∈ A : P(x)}, {x | P(x)} the set of x such that P(x). Explained under: glossary entry: set builder notation. symbol Which symbol says: the set of x such that P(x)? {x ∈ A : P(x)}, {x | P(x)} (explained under: glossary entry: set builder notation) symbol reverse Read the symbol: ∅, { } the empty set. Explained under: glossary entry: empty set. symbol Which symbol says: the empty set? ∅, { } (explained under: glossary entry: empty set) symbol reverse Read the symbol: U, 𝒰, E, Ω the universal set (Ω also the class of ordinals, or ω₁). Explained under: glossary entry: universal set. symbol Which symbol says: the universal set (Ω also the class of ordinals, or ω₁)? U, 𝒰, E, Ω (explained under: glossary entry: universal set) symbol reverse Read the symbol: ⊆ ⊂ ⊊ ⊇ ⊃ ⊄ ⊉ subset, proper subset (two conventions), superset, and their negations. Explained under: glossary entry: symbols. symbol Which symbol says: subset, proper subset (two conventions), superset, and their negations? ⊆ ⊂ ⊊ ⊇ ⊃ ⊄ ⊉ (explained under: glossary entry: symbols) symbol reverse Read the symbol: A = B the same members, by extensionality. Explained under: glossary entry: extensionality. symbol Which symbol says: the same members, by extensionality? A = B (explained under: glossary entry: extensionality) symbol reverse Read the symbol: ∪ ∩ union, intersection; ∪𝓕 and ∩𝓕 over a family. Explained under: algebra of sets. symbol Which symbol says: union, intersection; ∪𝓕 and ∩𝓕 over a family? ∪ ∩ (explained under: algebra of sets) symbol reverse Read the symbol: ∖ − difference, A ∖ B = {x ∈ A : x ∉ B}. Explained under: algebra of sets. symbol Which symbol says: difference, A ∖ B = {x ∈ A : x ∉ B}? ∖ − (explained under: algebra of sets) symbol reverse Read the symbol: A′ Aᶜ Ā U − A complement within the universal set. Explained under: glossary entry: complement. symbol Which symbol says: complement within the universal set? A′ Aᶜ Ā U − A (explained under: glossary entry: complement) symbol reverse Read the symbol: △ ⊕ symmetric difference. Explained under: glossary entry: symmetric difference. symbol Which symbol says: symmetric difference? △ ⊕ (explained under: glossary entry: symmetric difference) symbol reverse Read the symbol: A × B Cartesian product, the set of ordered pairs. Explained under: glossary entry: cartesian product. symbol Which symbol says: Cartesian product, the set of ordered pairs? A × B (explained under: glossary entry: cartesian product) symbol reverse Read the symbol: (a, b), ⟨a, b⟩ ordered pair. Explained under: glossary entry: ordered pair. symbol Which symbol says: ordered pair? (a, b), ⟨a, b⟩ (explained under: glossary entry: ordered pair) symbol reverse Read the symbol: (x₁, y₁), (x₂, y₂); p = (p₁, p₂), q = (q₁, q₂) a point by its coordinates: Sullivan numbers the points and letters the axes, Wikipedia and linear algebra letter the points and number the axes, so x₂ is q₁. Explained under: distance in n dimensions. symbol Which symbol says: a point by its coordinates: Sullivan numbers the points and letters the axes, Wikipedia and linear algebra letter the points and number the axes, so x₂ is q₁? (x₁, y₁), (x₂, y₂); p = (p₁, p₂), q = (q₁, q₂) (explained under: distance in n dimensions) symbol reverse Read the symbol: 𝒫(A), 2ᴬ power set. Explained under: glossary entry: power set. symbol Which symbol says: power set? 𝒫(A), 2ᴬ (explained under: glossary entry: power set) symbol reverse Read the symbol: |A|, n(A), #A, card(A) cardinality. Explained under: glossary entry: cardinality. symbol Which symbol says: cardinality? |A|, n(A), #A, card(A) (explained under: glossary entry: cardinality) symbol reverse Read the symbol: ℵ₀, ℵ₁, ℶ₁, 𝔠, κ⁺, ℷ infinite cardinals, the continuum, successor, gimel. Explained under: glossary entry: aleph beth and the continuum c. symbol Which symbol says: infinite cardinals, the continuum, successor, gimel? ℵ₀, ℵ₁, ℶ₁, 𝔠, κ⁺, ℷ (explained under: glossary entry: aleph beth and the continuum c) symbol reverse Read the symbol: ω, ω₁, ε₀, α + 1, S(α) ordinals and successors. Explained under: glossary entry: ordinal. symbol Which symbol says: ordinals and successors? ω, ω₁, ε₀, α + 1, S(α) (explained under: glossary entry: ordinal) symbol reverse Read the symbol: ℕ ℤ ℚ ℝ ℂ the number sets. Explained under: glossary entry: number sets n z q r c. symbol Which symbol says: the number sets? ℕ ℤ ℚ ℝ ℂ (explained under: glossary entry: number sets n z q r c) symbol reverse Read the symbol: x R y, (x, y) ∈ R, dom R, ran R a relation and its domain and range. Explained under: glossary entry: relation. symbol Which symbol says: a relation and its domain and range? x R y, (x, y) ∈ R, dom R, ran R (explained under: glossary entry: relation) symbol reverse Read the symbol: f: A → B, x ↦ f(x), f[A], f⁻¹, g ∘ f function, image of a set, inverse, composition. Explained under: relations and functions. symbol Which symbol says: function, image of a set, inverse, composition? f: A → B, x ↦ f(x), f[A], f⁻¹, g ∘ f (explained under: relations and functions) symbol reverse Read the symbol: [x], A/~ equivalence class, quotient set. Explained under: glossary entry: equivalence relation. symbol Which symbol says: equivalence class, quotient set? [x], A/~ (explained under: glossary entry: equivalence relation) symbol reverse Read the symbol: ≤, <, ≺ on a poset partial order, strict order. Explained under: glossary entry: partial order. symbol Which symbol says: partial order, strict order? ≤, <, ≺ on a poset (explained under: glossary entry: partial order) symbol reverse Read the symbol: ≈, ~, ≼, |A| ≤ |B| equinumerous, injects into. Explained under: glossary entry: symbols. symbol Which symbol says: equinumerous, injects into? ≈, ~, ≼, |A| ≤ |B| (explained under: glossary entry: symbols) symbol reverse Read the symbol: κ → (λ)ⁿ_r partition relation. Explained under: glossary entry: partition relation arrow notation. symbol Which symbol says: partition relation? κ → (λ)ⁿ_r (explained under: glossary entry: partition relation arrow notation) symbol reverse Read the symbol: ∀ ∃ ∃! ∄ for all, there exists, exactly one, none. Explained under: glossary entry: quantifier. symbol Which symbol says: for all, there exists, exactly one, none? ∀ ∃ ∃! ∄ (explained under: glossary entry: quantifier) symbol reverse Read the symbol: ¬ ∧ ∨ ⇒ → ⇔ ↔ ⇏ not, and, or, implies, iff, does not imply. Explained under: glossary entry: connectives. symbol Which symbol says: not, and, or, implies, iff, does not imply? ¬ ∧ ∨ ⇒ → ⇔ ↔ ⇏ (explained under: glossary entry: connectives) symbol reverse Read the symbol: ⊢ ⊬ ⊨ ⊣ proves, does not prove, models; the reversed turnstile. Explained under: glossary entry: turnstile. symbol Which symbol says: proves, does not prove, models; the reversed turnstile? ⊢ ⊬ ⊨ ⊣ (explained under: glossary entry: turnstile) symbol reverse Read the symbol: ∴ ∵ therefore, because. Explained under: glossary entry: therefore and because. symbol Which symbol says: therefore, because? ∴ ∵ (explained under: glossary entry: therefore and because) symbol reverse Read the symbol: ∎ ■ □ end of proof. Explained under: glossary entry: end of proof qed. symbol Which symbol says: end of proof? ∎ ■ □ (explained under: glossary entry: end of proof qed) symbol reverse Read the symbol: := :⟺ ≝ is defined as (a term, a statement). Explained under: README.md#three-books-three-notations. symbol Which symbol says: is defined as (a term, a statement)? := :⟺ ≝ (explained under: README.md#three-books-three-notations) symbol reverse Read the symbol: ≃ equality inside Cori and Lascar's formal language. Explained under: reading a formula. symbol Which symbol says: equality inside Cori and Lascar's formal language? ≃ (explained under: reading a formula) symbol reverse