what are the symbols of mathematics?

Answer 1

there are ever so many of them.these are used to represent mathematical operations and quantities easily and with least efforts and universally so that any mathematician from any part of the world can understand them the same way without ambiguity

Answer 2

This is all I know,

= equality x = y means x and y represent the same thing or value. 1 + 1 = 2
is equal to; equals
everywhere
≠

<>

!= inequation x ≠ y means that x and y do not represent the same thing or value. 1 ≠ 2
is not equal to; does not equal
everywhere
<

>

≪

≫ strict inequality x < y means x is less than y.

x > y means x is greater than y.

x ≪ y means x is much less than y.

x ≫ y means x is much greater than y. 3 < 4
5 > 4.

0.003 ≪ 1000000

is less than, is greater than, is much less than, is much greater than
order theory
≤

≥ inequality x ≤ y means x is less than or equal to y.

x ≥ y means x is greater than or equal to y. 3 ≤ 4 and 5 ≤ 5
5 ≥ 4 and 5 ≥ 5
is less than or equal to, is greater than or equal to
order theory
∝ proportionality y ∝ x means that y = kx for some constant k. if y = 2x, then y ∝ x
is proportional to
everywhere
+ addition 4 + 6 means the sum of 4 and 6. 2 + 7 = 9
plus
arithmetic
disjoint union A1 + A2 means the disjoint union of sets A1 and A2. A1 = {1, 2, 3, 4} ∧ A2 = {2, 4, 5, 7} ⇒
A1 + A2 = {(1,1), (2,1), (3,1), (4,1), (2,2), (4,2), (5,2), (7,2)}
the disjoint union of ... and ...
set theory
− subtraction 9 − 4 means the subtraction of 4 from 9. 8 − 3 = 5
minus
arithmetic
negative sign −3 means the negative of the number 3. −(−5) = 5
negative ; minus
arithmetic
set-theoretic complement A − B means the set that contains all the elements of A that are not in B. {1,2,4} − {1,3,4} = {2}
minus; without
set theory
× multiplication 3 × 4 means the multiplication of 3 by 4. 7 × 8 = 56
times
arithmetic
Cartesian product 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. {1,2} × {3,4} = {(1,3),(1,4),(2,3),(2,4)}
the Cartesian product of ... and ...; the direct product of ... and ...
set theory
cross product u × v means the cross product of vectors u and v (1,2,5) × (3,4,−1) =
(−22, 16, − 2)
cross
vector algebra
· multiplication 3 · 4 means the multiplication of 3 by 4. 7 · 8 = 56
times
arithmetic
dot product u · v means the dot product of vectors u and v (1,2,5) · (3,4,−1) = 6
dot
vector algebra
÷

⁄ division 6 ÷ 3 or 6 ⁄ 3 means the division of 6 by 3. 2 ÷ 4 = .5

12 ⁄ 4 = 3
divided by
arithmetic
±

∓ plus-minus 6 ± 3 means 6 + 3 or 6 - 3.
6 ± 3 ∓ 5 means 6 + 3 - 5 or 6 - 3 + 5. 6 ± 3 = 9 or 3
6 ± 3 ∓ 5 = 4 or 8
plus-minus; plus-or-minus
minus-plus; minus-or-plus
arithmetic
√ square root √x means the positive number whose square is x. √4 = 2
the principal square root of; square root
real numbers
complex square root if z = r exp(iφ) is represented in polar coordinates with -π < φ ≤ π, then √z = √r exp(iφ/2). √(-1) = i
the complex square root of; square root
complex numbers
| | absolute value |x| means the distance in the real line (or the complex plane) between x and zero. |3| = 3, |-5| = |5|
|i| = 1, |3+4i| = 5
absolute value of
numbers
Euclidean distance |x-y| means the Euclidean distance between x and y. If x=(1,1), and y=(4,5), then |x-y| = √((1-4)2+(1-5)2)=5
Euclidean distance between; Euclidean norm of
Geometry
| divides A single vertical bar is used to denote divisibility.
a|b means a divides b. Since 15 = 3×5, it is true that 3|15 and 5|15.
divides
Number Theory
! factorial n! is the product 1 × 2× ... × n. 4! = 1 × 2 × 3 × 4 = 24
factorial
combinatorics
~ probability distribution X ~ D, means the random variable X has the probability distribution D. X ~ N(0,1), the standard normal distribution
has distribution
statistics
⇒

→

⊃ material implication A ⇒ B means if A is true then B is also true; if A is false then nothing is said about B.

→ may mean the same as ⇒, or it may have the meaning for functions given below.

⊃ may mean the same as ⇒, or it may have the meaning for superset given below. x = 2 ⇒ x2 = 4 is true, but x2 = 4 ⇒ x = 2 is in general false (since x could be −2).
implies; if .. then
propositional logic
⇔

↔ material equivalence A ⇔ B means A is true if B is true and A is false if B is false. x + 5 = y +2 ⇔ x + 3 = y
if and only if; iff
propositional logic
¬

˜ logical negation The statement ¬A is true if and only if A is false.

A slash placed through another operator is the same as "¬" placed in front. ¬(¬A) ⇔ A
x ≠ y ⇔ ¬(x = y)
not
propositional logic
∧ logical conjunction or meet in a lattice 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)). n < 4 ∧ n >2 ⇔ n = 3 when n is a natural number.
and; min
propositional logic, lattice theory
∨ logical disjunction or join in a lattice 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)). n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number.
or; max
propositional logic, lattice theory


⊕



⊻ exclusive or The statement A ⊕ B is true when either A or B, but not both, are true. A ⊻ B means the same. (¬A) ⊕ A is always true, A ⊕ A is always false.
xor
propositional logic, Boolean algebra
direct sum The direct sum is a special way of combining several one modules into one general module (the symbol ⊕ is used, ⊻ is only for logic).

Most commonly, for vector spaces U, V, and W, the following consequence is used:
U = V ⊕ W ⇔ (U = V + W) ∧ (V ∩ W = ∅)
direct sum of
Abstract algebra
∀ universal quantification ∀ x: P(x) means P(x) is true for all x. ∀ n ∈ N: n2 ≥ n.
for all; for any; for each
predicate logic
∃ existential quantification ∃ x: P(x) means there is at least one x such that P(x) is true. ∃ n ∈ N: n is even.
there exists
predicate logic
∃! uniqueness quantification ∃! x: P(x) means there is exactly one x such that P(x) is true. ∃! n ∈ N: n + 5 = 2n.
there exists exactly one
predicate logic
:=

≡

:⇔ definition x := y or x ≡ y means x is defined to be another name for y (but note that ≡ can also mean other things, such as congruence).

P :⇔ Q means P is defined to be logically equivalent to Q. cosh x := (1/2)(exp x + exp (−x))

A XOR B :⇔ (A ∨ B) ∧ ¬(A ∧ B)
is defined as
everywhere
≅ congruence △ABC ≅ △DEF means triangle ABC is congruent to triangle DEF.
is congruent to
geometry
{ , } set brackets {a,b,c} means the set consisting of a, b, and c. N = {0, 1, 2, ...}
the set of ...
set theory
{ : }

{ | } set builder notation {x : P(x)} means the set of all x for which P(x) is true. {x | P(x)} is the same as {x : P(x)}. {n ∈ N : n2 < 20} = {0, 1, 2, 3, 4}
the set of ... such that ...
set theory


∅

{} empty set ∅ means the set with no elements. {} means the same. {n ∈ N : 1 < n2 < 4} = ∅
the empty set
set theory
∈

∉ set membership a ∈ S means a is an element of the set S; a ∉ S means a is not an element of S. (1/2)−1 ∈ N

2−1 ∉ N
is an element of; is not an element of
everywhere, set theory
⊆

⊂ subset (subset) A ⊆ B means every element of A is also element of B.

(proper subset) A ⊂ B means A ⊆ B but A ≠ B. A ∩ B ⊆ A; Q ⊂ R
is a subset of
set theory
⊇

⊃ superset A ⊇ B means every element of B is also element of A.

A ⊃ B means A ⊇ B but A ≠ B. A ∪ B ⊇ B; R ⊃ Q
is a superset of
set theory
∪ set-theoretic union (exclusive) A ∪ B means the set that contains all the elements from A, or all the elements from B, but not both.
"A or B, but not both".

(inclusive) A ∪ B means the set that contains all the elements from A, or all the elements from B, or all the elements from both A and B.
"A or B or both". A ⊆ B ⇔ A ∪ B = B (inclusive)
the union of ... and ...; union
set theory
∩ set-theoretic intersection A ∩ B means the set that contains all those elements that A and B have in common. {x ∈ R : x2 = 1} ∩ N = {1}
intersected with; intersect
set theory
Δ symmetric difference AΔB means the set of elements in exactly one of A or B. {1,5,6,8}Δ {2,5,8} = {1,2,6}
symmetric difference
set theory
∖ set-theoretic complement A ∖ B means the set that contains all those elements of A that are not in B. {1,2,3,4} ∖ {3,4,5,6} = {1,2}
minus; without
set theory
( ) function application f(x) means the value of the function f at the element x. If f(x) := x2, then f(3) = 32 = 9.
of
set theory
precedence grouping Perform the operations inside the parentheses first. (8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4.
parentheses
everywhere
f:X→Y function arrow f: X → Y means the function f maps the set X into the set Y. Let f: Z → N be defined by f(x) := x2.
from ... to
set theory
o function composition fog is the function, such that (fog)(x) = f(g(x)). if f(x) := 2x, and g(x) := x + 3, then (fog)(x) = 2(x + 3).
composed with
set theory


N


ℕ natural numbers N means {0, 1, 2, 3, ...}, but see the article on natural numbers for a different convention. {|a| : a ∈ Z} = N
N
numbers


Z


ℤ integers Z means {..., −3, −2, −1, 0, 1, 2, 3, ...}. {a, -a : a ∈ N} = Z
Z
numbers


Q


ℚ rational numbers Q means {p/q : p,q ∈ Z, q ≠ 0}. 3.14 ∈ Q

π ∉ Q
Q
numbers


R


ℝ real numbers R means the set of real numbers. π ∈ R

√(−1) ∉ R
R
numbers


C


ℂ complex numbers C means {a + bi : a,b ∈ R}. i = √(−1) ∈ C
C
numbers
arbitrary constant C can be any number, most likely unknown; usually occurs when calculating antiderivatives. if f(x) = 6x² + 4x, then F(x) = 2x³ + 2x² + C
C
integral calculus
∞ infinity ∞ is an element of the extended number line that is greater than all real numbers; it often occurs in limits. limx→0 1/|x| = ∞
infinity
numbers
π pi π is the ratio of a circle's circumference to its diameter. Its value is 3.1415.... A = πr² is the area of a circle with radius r
pi
Euclidean geometry
|| || norm ||x|| is the norm of the element x of a normed vector space. ||x+y|| ≤ ||x|| + ||y||
norm of; length of
linear algebra
∑ summation means a1 + a2 + ... + an.
= 12 + 22 + 32 + 42


= 1 + 4 + 9 + 16 = 30
sum over ... from ... to ... of
arithmetic
∏ product means a1a2···an.
= (1+2)(2+2)(3+2)(4+2)

= 3 × 4 × 5 × 6 = 360
product over ... from ... to ... of
arithmetic
Cartesian product means the set of all (n+1)-tuples

(y0,...,yn).

the Cartesian product of; the direct product of
set theory
∐ coproduct
coproduct over ... from ... to ... of
category theory
′ derivative f ′(x) is the derivative of the function f at the point x, i.e., the slope of the tangent to f at x. If f(x) := x2, then f ′(x) = 2x
... prime; derivative of ...
calculus
∫ indefinite integral or antiderivative ∫ f(x) dx means a function whose derivative is f. ∫x2 dx = x3/3 + C
indefinite integral of ...;; the antiderivative of ...
calculus
definite integral ∫ab f(x) dx means the signed area between the x-axis and the graph of the function f between x = a and x = b. ∫0b x2 dx = b3/3;
integral from ... to ... of ... with respect to
calculus
∇ gradient ∇f (x1, …, xn) is the vector of partial derivatives (∂f / ∂x1, …, ∂f / ∂xn). If f (x,y,z) := 3xy + z², then ∇f = (3y, 3x, 2z)
del, nabla, gradient of
calculus
∂ partial derivative With f (x1, …, xn), ∂f/∂xi is the derivative of f with respect to xi, with all other variables kept constant. If f(x,y) := x2y, then ∂f/∂x = 2xy
partial derivative of
calculus
boundary ∂M means the boundary of M ∂{x : ||x|| ≤ 2} = {x : ||x|| = 2}
boundary of
topology
⊥ perpendicular x ⊥ y means x is perpendicular to y; or more generally x is orthogonal to y. If l ⊥ m and m ⊥ n then l || n.
is perpendicular to
geometry
bottom element x = ⊥ means x is the smallest element. ∀x : x ∧ ⊥ = ⊥
the bottom element
lattice theory
|| parallel x || y means x is parallel to y. If l || m and m ⊥ n then l ⊥ n.
is parallel to
geometry
⊧ entailment A ⊧ B means the sentence A entails the sentence B, that is every model in which A is true, B is also true. A ⊧ A ∨ ¬A
entails
model theory
⊢ inference x ⊢ y means y is derived from x. A → B ⊢ ¬B → ¬A
infers or is derived from
propositional logic, predicate logic
◅ normal subgroup N ◅ G means that N is a normal subgroup of group G. Z(G) ◅ G
is a normal subgroup of
group theory
/ quotient group G/H means the quotient of group G modulo its subgroup H. {0, a, 2a, b, b+a, b+2a} / {0, b} = {{0, b}, {a, b+a}, {2a, b+2a}}
mod
group theory
quotient set A/~ means the set of all ~ equivalence classes in A.

set theory
≈ isomorphism G ≈ H means that group G is isomorphic to group H Q / {1, −1} ≈ V,
where Q is the quaternion group and V is the Klein four-group.
is isomorphic to
group theory
approximately equal x ≈ y means x is approximately equal to y π ≈ 3.14159
is approximately equal to
everywhere
<,> inner product means the inner product between x and y, as defined in an inner product space. The standard inner product between two vectors x = (2, 3) and y = (-1, 5) is:
= 2×-1 + 3×5 = 13
inner product of
vector algebra
⊗ tensor product V ⊗ U means the tensor product of V and U. {1, 2, 3, 4} ⊗ {1,1,2} =
{{1, 2, 3, 4}, {1, 2, 3, 4}, {2, 4, 6, 8}}

If you weant the same information in an organised fashion go to,

Answer 3

What kind of symbols are you looking for? You can give me any letter or crazy shape from many languages and there is a very good chance that it will be a mathematical symbol.

Answer 4

That depends on what you are looking for. For example +/- / * are symbols for addition subtraction division and multiplication.
a b c are generally for constant x y z for variables.

0 1 2 3 etc for digits

Answer 5

A symbol is a higher abstract way of thinking.Human beings can do it.

You write a symbol and with this You can define a group of expressions, words, numbers...

One Symbol combines things with certain, defined characteristics or attributes!

Answer 6

This is a case of language barrier.

I think you wish to know why are they used?

Many reasons, most symbols are universally recognised and hence, over come lots of language problem.

EG.

+, -, =.

They are also use to make one statement or even number of statement.

EG

= this means "Equal to". It is a two word sentence, most people will understand.

Answer 7

Any symbol is defined and used to represent an item or process.

Answer 8

Σ= sigma
Ф= phi
ρ= rho
μ= Mu
β=beta
γ=gamma
ζ=zeta
η=eta
θ=theta
κ=kappa
λ=lambda
μ=mu
α=alpha
π=pi
Furhter x,y z a,b,c are also used for variables
!= factorials

Answer 9

r u a student of a open school / college / university etc., :-)...how did you get to think abt such a great question...i wonder....einstein effect !!!!!!

Answer 10

add., sub., div., multiply, square root, exponent, parentheses, greater than, less than, greater than or equal too, less than or equal too, // (Parallel), and ~ this means something i can't remember what.