<Tr> <Td> </Td> <Td> _̇ (\ displaystyle (\ dot (\,)) \! \,) </Td> <Td> derivative...dot; time derivative of calculus </Td> <Td> x _̇ (\ displaystyle (\ dot (x))) means the derivative of x with respect to time . That is x _̇ (t) = ∂ ∂ t x (t) (\ displaystyle (\ dot (x)) (t) = (\ frac (\ partial) (\ partial t)) x (t)). </Td> <Td> If x (t): = t, then x _̇ (t) = 2 t (\ displaystyle (\ dot (x)) (t) = 2t). </Td> </Tr> <Table> <Tr> <Th> Symbol in HTML </Th> <Th> Symbol in TeX </Th> <Th> Name </Th> <Th> Explanation </Th> <Th> Examples </Th> </Tr> <Tr> <Th> Read as </Th> </Tr> <Tr> <Th> Category <P> </P> </Th> </Tr> <Tr> <Td> ∀ </Td> <Td> ∀ (\ displaystyle \ forall \! \,) </Td> <Td> universal quantification for all; for any; for each; for every predicate logic </Td> <Td> ∀ x: P (x) means P (x) is true for all x . </Td> <Td> ∀ n ∈ N: n ≥ n . </Td> </Tr> <Tr> <Td> B </Td> <Td> B (\ displaystyle \ mathbb (B) \! \,) B (\ displaystyle \ mathbf (B) \! \,) </Td> <Td> boolean domain B; the (set of) boolean values; the (set of) truth values; set theory, boolean algebra </Td> <Td> B means either (0, 1), (false, true), (F, T), or (⊥, ⊤) (\ displaystyle \ left \ (\ bot, \ top \ right \)). </Td> <Td> (¬ False) ∈ B </Td> </Tr> <Tr> <Td> C </Td> <Td> C (\ displaystyle \ mathbb (C) \! \,) C (\ displaystyle \ mathbf (C) \! \,) </Td> <Td> complex numbers C; the (set of) complex numbers numbers </Td> <Td> C means (a + b i: a, b ∈ R). </Td> <Td> i = √ − 1 ∈ C </Td> </Tr> <Tr> <Td> c </Td> <Td> c (\ displaystyle (\ mathfrak (c)) \! \,) </Td> <Td> cardinality of the continuum cardinality of the continuum; c; cardinality of the real numbers set theory </Td> <Td> The cardinality of R (\ displaystyle \ mathbb (R)) is denoted by R (\ displaystyle \ mathbb (R)) or by the symbol c (\ displaystyle (\ mathfrak (c))) (a lowercase Fraktur letter C). </Td> <Td> c = ב 1 (\ displaystyle (\ mathfrak (c)) = (\ beth) _ (1)) <P> </P> </Td> </Tr> <Tr> <Td> ∂ </Td> <Td> ∂ (\ displaystyle \ partial \! \,) </Td> <Td> partial derivative partial; d calculus </Td> <Td> ∂ f / ∂ x means the partial derivative of f with respect to x, where f is a function on (x,..., x). </Td> <Td> If f (x, y): = x y, then ∂ f / ∂ x = 2xy, </Td> </Tr> <Tr> <Td> boundary boundary of topology </Td> <Td> ∂ M means the boundary of M </Td> <Td> ∂ (x: x ≤ 2) = (x: x = 2) </Td> </Tr> <Tr> <Td> degree of a polynomial degree of algebra </Td> <Td> ∂ f means the degree of the polynomial f . (This may also be written deg f .) </Td> <Td> ∂ (x − 1) = 2 </Td> </Tr> <Tr> <Td> E </Td> <Td> E (\ displaystyle \ mathbb (E)) E (\ displaystyle \ mathrm (E)) </Td> <Td> expected value expected value probability theory </Td> <Td> the value of a random variable one would "expect" to find if one could repeat the random variable process an infinite number of times and take the average of the values obtained </Td> <Td> E (X) = x 1 p 1 + x 2 p 2 + ⋯ + x k p k p 1 + p 2 + ⋯ + p k (\ displaystyle \ mathbb (E) (X) = (\ frac (x_ (1) p_ (1) + x_ (2) p_ (2) + \ dotsb + x_ (k) p_ (k)) (p_ (1) + p_ (2) + \ dotsb + p_ (k)))) </Td> </Tr> <Tr> <Td> ∃ </Td> <Td> ∃ (\ displaystyle \ exists \! \,) </Td> <Td> existential quantification there exists; there is; there are predicate logic </Td> <Td> ∃ x: P (x) means there is at least one x such that P (x) is true . </Td> <Td> ∃ n ∈ N: n is even . </Td> </Tr> <Tr> <Td> ∃! </Td> <Td> ∃! (\ displaystyle \ exists! \! \,) </Td> <Td> uniqueness quantification there exists exactly one predicate logic </Td> <Td> ∃! x: P (x) means there is exactly one x such that P (x) is true . </Td> <Td> ∃! n ∈ N: n + 5 = 2n . </Td> </Tr> <Tr> <Td> ∈ ∉ </Td> <Td> ∈ (\ displaystyle \ in \! \,) ∉ (\ displaystyle \ notin \! \,) </Td> <Td> set membership is an element of; is not an element of everywhere, set theory </Td> <Td> a ∈ S means a is an element of the set S; a ∉ S means a is not an element of S . </Td> <Td> (1 / 2) ∈ N 2 ∉ N </Td> </Tr> <Tr> <Td> ∌ </Td> <Td> ∌ (\ displaystyle \ not \ ni) </Td> <Td> set membership does not contain as an element set theory </Td> <Td> S ∌ e means the same thing as e ∉ S, where S is a set and e is not an element of S . </Td> <Td> </Td> </Tr> <Tr> <Td> ∋ </Td> <Td> ∋ (\ displaystyle \ ni) </Td> <Td> such that symbol such that mathematical logic </Td> <Td> often abbreviated as "s.t.";: and are also used to abbreviate "such that". The use of ∋ goes back to early mathematical logic and its usage in this sense is declining . The symbol ∍ (\ displaystyle \ backepsilon) ("back epsilon") is sometimes specifically used for "such that" to avoid confusion with set membership . </Td> <Td> Choose x (\ displaystyle x) ∋ 2 x (\ displaystyle x) and 3 x (\ displaystyle x). (Here is used in the sense of "divides".) </Td> </Tr> <Tr> <Td> set membership contains as an element set theory </Td> <Td> S ∋ e means the same thing as e ∈ S, where S is a set and e is an element of S . </Td> <Td> </Td> </Tr> <Tr> <Td> H </Td> <Td> H (\ displaystyle \ mathbb (H) \! \,) H (\ displaystyle \ mathbf (H) \! \,) </Td> <Td> quaternions or Hamiltonian quaternions H; the (set of) quaternions numbers </Td> <Td> H means (a + b i + c j + d k: a, b, c, d ∈ R). </Td> <Td> </Td> </Tr> <Tr> <Td> N </Td> <Td> N (\ displaystyle \ mathbb (N) \! \,) N (\ displaystyle \ mathbf (N) \! \,) </Td> <Td> natural numbers the (set of) natural numbers numbers </Td> <Td> N means either (0, 1, 2, 3, ...) or (1, 2, 3, ...). The choice depends on the area of mathematics being studied; e.g. number theorists prefer the latter; analysts, set theorists and computer scientists prefer the former . To avoid confusion, always check an author's definition of N . Set theorists often use the notation ω (for least infinite ordinal) to denote the set of natural numbers (including zero), along with the standard ordering relation ≤ . </Td> <Td> N = (a: a ∈ Z) or N = (a> 0: a ∈ Z) </Td> </Tr> <Tr> <Td> ○ </Td> <Td> ∘ (\ displaystyle \ circ) </Td> <Td> Hadamard product entrywise product linear algebra </Td> <Td> For two matrices (or vectors) of the same dimensions A, B ∈ R m × n (\ displaystyle A, B \ in (\ mathbb (R)) ^ (m \ times n)) the Hadamard product is a matrix of the same dimensions A ∘ B ∈ R m × n (\ displaystyle A \ circ B \ in (\ mathbb (R)) ^ (m \ times n)) with elements given by (A ∘ B) i, j = (A) i, j ⋅ (B) i, j (\ displaystyle (A \ circ B) _ (i, j) = (A) _ (i, j) \ cdot (B) _ (i, j)). </Td> <Td> (1 2 2 4) ∘ (1 2 0 0) = (1 4 0 0) (\ displaystyle (\ begin (bmatrix) 1&2 \ \ 2&4 \ \ \ end (bmatrix)) \ circ (\ begin (bmatrix) 1&2 \ \ 0&0 \ \ \ end (bmatrix)) = (\ begin (bmatrix) 1&4 \ \ 0&0 \ \ \ end (bmatrix))) </Td> </Tr> <Tr> <Td> ∘ </Td> <Td> ∘ (\ displaystyle \ circ \! \,) </Td> <Td> function composition composed with set theory </Td> <Td> f ∘ g is the function such that (f ∘ g) (x) = f (g (x)). </Td> <Td> if f (x): = 2x, and g (x): = x + 3, then (f ∘ g) (x) = 2 (x + 3). </Td> </Tr> <Tr> <Td> O </Td> <Td> O (\ displaystyle O) </Td> <Td> Big O notation big - oh of Computational complexity theory </Td> <Td> The Big O notation describes the limiting behavior of a function, when the argument tends towards a particular value or infinity . </Td> <Td> If f (x) = 6x − 2x + 5 and g (x) = x, then f (x) = O (g (x)) as x → ∞ (\ displaystyle f (x) = O (g (x)) (\ mbox (as)) x \ to \ infty \,) </Td> </Tr> <Tr> <Td> ∅ () </Td> <Td> ∅ (\ displaystyle \ emptyset \! \,) ∅ (\ displaystyle \ varnothing \! \,) () (\ displaystyle \ (\) \! \,) </Td> <Td> empty set the empty set null set set theory </Td> <Td> ∅ means the set with no elements . () means the same . </Td> <Td> (n ∈ N: 1 <n <4) = ∅ </Td> </Tr> <Tr> <Td> P </Td> <Td> P (\ displaystyle \ mathbb (P) \! \,) P (\ displaystyle \ mathbf (P) \! \,) </Td> <Td> set of primes P; the set of prime numbers arithmetic </Td> <Td> P is often used to denote the set of prime numbers . </Td> <Td> 2 ∈ P, 3 ∈ P, 8 ∉ P (\ displaystyle 2 \ in \ mathbb (P), 3 \ in \ mathbb (P), 8 \ notin \ mathbb (P)) </Td> </Tr> <Tr> <Td> projective space P; the projective space; the projective line; the projective plane topology </Td> <Td> P means a space with a point at infinity . </Td> <Td> P 1 (\ displaystyle \ mathbb (P) ^ (1)), P 2 (\ displaystyle \ mathbb (P) ^ (2)) </Td> </Tr> <Tr> <Td> probability the probability of probability theory </Td> <Td> P (X) means the probability of the event X occurring . This may also be written as P (X), Pr (X), P (X) or Pr (X). </Td> <Td> If a fair coin is flipped, P (Heads) = P (Tails) = 0.5 . </Td> </Tr> <Tr> <Td> Power set the Power set of Powerset </Td> <Td> Given a set S, the power set of S is the set of all subsets of the set S . The power set of S0 is <P> denoted by P (S). </P> </Td> <Td> The power set P ((0, 1, 2)) is the set of all subsets of (0, 1, 2). Hence, <P> P ((0, 1, 2)) = (∅, (0), (1), (2), (0, 1), (0, 2), (1, 2), (0, 1, 2)). </P> </Td> </Tr> <Tr> <Td> Q Q </Td> <Td> Q (\ displaystyle \ mathbb (Q) \! \,) Q (\ displaystyle \ mathbf (Q) \! \,) </Td> <Td> rational numbers Q; the (set of) rational numbers; the rationals numbers </Td> <Td> Q means (p / q: p ∈ Z, q ∈ N). </Td> <Td> 3.14000...∈ Q π ∉ Q <P> </P> </Td> </Tr> <Tr> <Td> R </Td> <Td> R (\ displaystyle \ mathbb (R) \! \,) R (\ displaystyle \ mathbf (R) \! \,) </Td> <Td> real numbers R; the (set of) real numbers; the reals numbers </Td> <Td> R means the set of real numbers . </Td> <Td> π ∈ R √ (− 1) ∉ R <P> </P> </Td> </Tr> <Tr> <Td> </Td> <Td> † (\ displaystyle () ^ (\ dagger) \! \,) </Td> <Td> conjugate transpose conjugate transpose; adjoint; Hermitian adjoint / conjugate / transpose / dagger matrix operations </Td> <Td> A means the transpose of the complex conjugate of A . This may also be written A, A, A, A or A . </Td> <Td> If A = (a) then A = (a). </Td> </Tr> <Tr> <Td> </Td> <Td> T (\ displaystyle () ^ (\ mathsf (T)) \! \,) </Td> <Td> transpose transpose matrix operations </Td> <Td> A means A, but with its rows swapped for columns . This may also be written A ′, A or A . </Td> <Td> If A = (a) then A = (a). </Td> </Tr> <Tr> <Td> ⊤ </Td> <Td> ⊤ (\ displaystyle \ top \! \,) </Td> <Td> top element the top element lattice theory </Td> <Td> ⊤ means the largest element of a lattice . </Td> <Td> ∀ x: x ∨ ⊤ = ⊤ </Td> </Tr> <Tr> <Td> top type the top type; top type theory </Td> <Td> ⊤ means the top or universal type; every type in the type system of interest is a subtype of top . </Td> <Td> ∀ types T, T <: ⊤ </Td> </Tr> <Tr> <Td> ⊥ </Td> <Td> ⊥ (\ displaystyle \ bot \! \,) </Td> <Td> perpendicular is perpendicular to geometry </Td> <Td> x ⊥ y means x is perpendicular to y; or more generally x is orthogonal to y . </Td> <Td> If l ⊥ m and m ⊥ n in the plane, then l n . </Td> </Tr> <Tr> <Td> orthogonal complement orthogonal / perpendicular complement of; perp linear algebra </Td> <Td> W means the orthogonal complement of W (where W is a subspace of the inner product space V), the set of all vectors in V orthogonal to every vector in W . </Td> <Td> Within R 3 (\ displaystyle \ mathbb (R) ^ (3)), (R 2) ⊥ ≅ R (\ displaystyle (\ mathbb (R) ^ (2)) ^ (\ perp) \ cong \ mathbb (R)). </Td> </Tr> <Tr> <Td> coprime is coprime to number theory </Td> <Td> x ⊥ y means x has no factor greater than 1 in common with y . </Td> <Td> 34 ⊥ 55 </Td> </Tr> <Tr> <Td> independent is independent of probability </Td> <Td> A ⊥ B means A is an event whose probability is independent of event B . The double perpendicular symbol (⊥ ⊥ (\ displaystyle \ perp \! \! \! \ perp)) is also commonly used for the purpose of denoting this, for instance: A ⊥ ⊥ B (\ displaystyle A \ perp \! \! \! \ perp B) </Td> <Td> If A ⊥ B, then P (A B) = P (A). </Td> </Tr> <Tr> <Td> bottom element the bottom element lattice theory </Td> <Td> ⊥ means the smallest element of a lattice . </Td> <Td> ∀ x: x ∧ ⊥ = ⊥ </Td> </Tr> <Tr> <Td> bottom type the bottom type; bot type theory </Td> <Td> ⊥ means the bottom type (a.k.a. the zero type or empty type); bottom is the subtype of every type in the type system . </Td> <Td> ∀ types T, ⊥ <: T </Td> </Tr> <Tr> <Td> comparability is comparable to order theory </Td> <Td> x ⊥ y means that x is comparable to y . </Td> <Td> (e, π) ⊥ (1, 2, e, 3, π) under set containment . <P> </P> </Td> </Tr> <Tr> <Td> U U </Td> <Td> U (\ displaystyle \ mathbb (U) \! \,) U (\ displaystyle \ mathbf (U) \! \,) </Td> <Td> all numbers being considered U; the universal set; the set of all numbers; all numbers considered set theory </Td> <Td> U means "the set of all elements being considered ." It may represent all numbers both real and complex, or any subset of these--hence the term "universal". </Td> <Td> U = (R, C) includes all numbers . If instead, U = (Z, C), then π ∉ U . </Td> </Tr> <Tr> <Td> ∪ </Td> <Td> ∪ (\ displaystyle \ cup \! \,) </Td> <Td> set - theoretic union the union of...or ...; union set theory </Td> <Td> A ∪ B means the set of those elements which are either in A, or in B, or in both . </Td> <Td> A ⊆ B ⇔ (A ∪ B) = B </Td> </Tr> <Tr> <Td> ∩ </Td> <Td> ∩ (\ displaystyle \ cap \! \,) </Td> <Td> set - theoretic intersection intersected with; intersect set theory </Td> <Td> A ∩ B means the set that contains all those elements that A and B have in common . </Td> <Td> (x ∈ R: x = 1) ∩ N = (1) </Td> </Tr> <Tr> <Td> ∨ </Td> <Td> ∨ (\ displaystyle \ lor \! \,) </Td> <Td> logical disjunction or join in a lattice or; max; join propositional logic, lattice theory </Td> <Td> The statement A ∨ B is true if A or B (or both) are true; if both are false, the statement is false . For functions A (x) and B (x), A (x) ∨ B (x) is used to mean max (A (x), B (x)). </Td> <Td> n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number . </Td> </Tr> <Tr> <Td> ∧ </Td> <Td> ∧ (\ displaystyle \ land \! \,) </Td> <Td> logical conjunction or meet in a lattice and; min; meet propositional logic, lattice theory </Td> <Td> The statement A ∧ B is true if A and B are both true; else it is false . For functions A (x) and B (x), A (x) ∧ B (x) is used to mean min (A (x), B (x)). </Td> <Td> n <4 ∧ n> 2 ⇔ n = 3 when n is a natural number . </Td> </Tr> <Tr> <Td> wedge product wedge product; exterior product exterior algebra </Td> <Td> u ∧ v means the wedge product of any multivectors u and v. In three - dimensional Euclidean space the wedge product and the cross product of two vectors are each other's Hodge dual . </Td> <Td> u ∧ v = ∗ (u × v) if u, v ∈ R 3 (\ displaystyle u \ wedge v = * (u \ times v) \ (\ text (if)) u, v \ in \ mathbb (R) ^ (3)) </Td> </Tr> <Tr> <Td> × </Td> <Td> × (\ displaystyle \ times \! \,) </Td> <Td> multiplication times; multiplied by arithmetic </Td> <Td> 3 × 4 means the multiplication of 3 by 4 . (The symbol * is generally used in programming languages, where ease of typing and use of ASCII text is preferred .) </Td> <Td> 7 × 8 = 56 </Td> </Tr> <Tr> <Td> Cartesian product the Cartesian product of...and ...; the direct product of...and...set theory </Td> <Td> X × Y means the set of all ordered pairs with the first element of each pair selected from X and the second element selected from Y . </Td> <Td> (1, 2) × (3, 4) = ((1, 3), (1, 4), (2, 3), (2, 4)) </Td> </Tr> <Tr> <Td> cross product cross linear algebra </Td> <Td> u × v means the cross product of vectors u and v </Td> <Td> (1, 2, 5) × (3, 4, − 1) = (− 22, 16, − 2) </Td> </Tr> <Tr> <Td> group of units the group of units of ring theory </Td> <Td> R consists of the set of units of the ring R, along with the operation of multiplication . This may also be written R as described below, or U (R). </Td> <Td> (Z / 5 Z) × = ((1), (2), (3), (4)) ≅ C 4 (\ displaystyle (\ begin (aligned) (\ mathbb (Z) / 5 \ mathbb (Z)) ^ (\ times) & = \ ((1), (2), (3), (4) \) \ \ & \ cong \ mathrm (C) _ (4) \ \ \ end (aligned))) </Td> </Tr> <Tr> <Td> ⊗ </Td> <Td> ⊗ (\ displaystyle \ otimes \! \,) </Td> <Td> tensor product, tensor product of modules tensor product of linear algebra </Td> <Td> V ⊗ U (\ displaystyle V \ otimes U) means the tensor product of V and U. V ⊗ R U (\ displaystyle V \ otimes _ (R) U) means the tensor product of modules V and U over the ring R . </Td> <Td> (1, 2, 3, 4) ⊗ (1, 1, 2) = ((1, 1, 2), (2, 2, 4), (3, 3, 6), (4, 4, 8)) </Td> </Tr> <Tr> <Td> ⋉ ⋊ </Td> <Td> ⋉ (\ displaystyle \ ltimes \! \,) ⋊ (\ displaystyle \ rtimes \! \,) </Td> <Td> semidirect product the semidirect product of group theory </Td> <Td> N ⋊ H is the semidirect product of N (a normal subgroup) and H (a subgroup), with respect to φ . Also, if G = N ⋊ H, then G is said to split over N . (⋊ may also be written the other way round, as ⋉, or as × .) </Td> <Td> D 2 n ≅ C n ⋊ C 2 (\ displaystyle D_ (2n) \ cong \ mathrm (C) _ (n) \ rtimes \ mathrm (C) _ (2)) </Td> </Tr> <Tr> <Td> semijoin the semijoin of relational algebra </Td> <Td> R ⋉ S is the semijoin of the relations R and S, the set of all tuples in R for which there is a tuple in S that is equal on their common attribute names . </Td> <Td> R ⋉ (\ displaystyle \ ltimes) S = Π (\ displaystyle \ Pi) (R ⋈ (\ displaystyle \ bowtie) S) </Td> </Tr> <Tr> <Td> ⋈ </Td> <Td> ⋈ (\ displaystyle \ bowtie \! \,) </Td> <Td> natural join the natural join of relational algebra </Td> <Td> R ⋈ S is the natural join of the relations R and S, the set of all combinations of tuples in R and S that are equal on their common attribute names . </Td> <Td> <P> </P> </Td> </Tr> <Tr> <Td> Z Z </Td> <Td> Z (\ displaystyle \ mathbb (Z) \! \,) Z (\ displaystyle \ mathbf (Z) \! \,) </Td> <Td> integers the (set of) integers numbers </Td> <Td> Z means (..., − 3, − 2, − 1, 0, 1, 2, 3, ...). <P> Z or Z means (1, 2, 3, ...). Z means (0, 1, 2, 3, ...). Z is used by some authors to mean (0, 1, 2, 3, ...) and others to mean (... - 2, - 1, 1, 2, 3, ...). </P> </Td> <Td> Z = (p, − p: p ∈ N ∪ (0) ​) </Td> </Tr> <Tr> <Td> Z Z Z Z </Td> <Td> Z n (\ displaystyle \ mathbb (Z) _ (n) \! \,) Z p (\ displaystyle \ mathbb (Z) _ (p) \! \,) Z n (\ displaystyle \ mathbf (Z) _ (n) \! \,) Z p (\ displaystyle \ mathbf (Z) _ (p) \! \,) </Td> <Td> integers mod n the (set of) integers modulo n numbers </Td> <Td> Z means ((0), (1), (2),...(n − 1)) with addition and multiplication modulo n . Note that any letter may be used instead of n, such as p . To avoid confusion with p - adic numbers, use Z / pZ or Z / (p) instead . </Td> <Td> Z = ((0), (1), (2)) </Td> </Tr> <Tr> <Td> p - adic integers the (set of) p - adic integers numbers </Td> <Td> Note that any letter may be used instead of p, such as n or l . </Td> <Td> </Td> </Tr> </Table> <Tr> <Th> Symbol in HTML </Th> <Th> Symbol in TeX </Th> <Th> Name </Th> <Th> Explanation </Th> <Th> Examples </Th> </Tr> <Tr> <Th> Read as </Th> </Tr>

What is the meaning of divisible in mathematics