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Daftar Simbol Matematika

Dalam matematika sering digunakan simbol-simbol yang umum dikenal oleh matematikawan. Sering kali pengertian simbol ini tidak dijelaskan, karena dianggap maknanya telah diketahui. Hal ini kadang menyulitkan bagi mereka yang awam. Daftar berikut ini berisi banyak simbol beserta artinya.


Simbol
Nama Penjelasan Contoh
Dibaca sebagai
Kategori
=
kesamaan x = y berarti x and y mewakili hal atau nilai yang sama. 1 + 1 = 2
sama dengan
umum
Ketidaksamaan xy berarti x dan y tidak mewakili hal atau nilai yang sama. 1 ≠ 2
tidak sama dengan
umum
< >
ketidaksamaan x < y berarti x lebih kecil dari y.

x > y means x lebih besar dari y.
3 <> 4
lebih kecil dari; lebih besar dari
order theory


inequality xy berarti x lebih kecil dari atau sama dengan y.

xy means x lebih besar dari atau sama dengan y.
3 ≤ 4 and 5 ≤ 5
5 ≥ 4 and 5 ≥ 5
lebih kecil dari atau sama dengan, lebih besar dari atau sama dengan
order theory
+
tambah 4 + 6 berarti jumlah antara 4 dan 6. 2 + 7 = 9
tambah
aritmatika
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 …
teori himpunan
kurang 9 − 4 berarti 9 dikurangi 4. 8 − 3 = 5
kurang
aritmatika
tanda negatif −3 berarti negatif dari angka 3. −(−5) = 5
negatif
aritmatika
set-theoretic complement AB 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
kali
aritmatika
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 …
teori himpunan
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
÷

/
division 6 ÷ 3 atau 6/3 berati 6 dibagi 3. 2 ÷ 4 = .5

12/4 = 3
bagi
aritmatika
square root x berarti bilangan positif yang kuadratnya x. √4 = 2
akar kuadrat
bilangan real
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
bilangan complex
| |
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
!
factorial n! is the product 1×2×...×n. 4! = 1 × 2 × 3 × 4 = 24
faktorial
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
statistika




material implication AB 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 AB 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
xy ⇔ ¬(x = y)
not
propositional logic
logical conjunction or meet in a lattice The statement AB is true if A and B are both true; else it is false. n <>n >2 ⇔ n = 3 when n is a natural number.
and
propositional logic, lattice theory
logical disjunction or join in a lattice The statement AB is true if A or B (or both) are true; if both are false, the statement is false. n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number.
or
propositional logic, lattice theory



exclusive or The statement AB is true when either A or B, but not both, are true. AB means the same. A) ⊕ A is always true, AA is always false.
xor
propositional logic, Boolean algebra
universal quantification x: P(x) means P(x) is true for all x. nN: n2n.
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. nN: n is even.
there exists
predicate logic
∃!
uniqueness quantification ∃! x: P(x) means there is exactly one x such that P(x) is true. ∃! nN: n + 5 = 2n.
there exists exactly one
predicate logic
:=



:⇔
definition x := y or xy 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 :⇔ (AB) ∧ ¬(AB)
is defined as
everywhere
{ , }
set brackets {a,b,c} means the set consisting of a, b, and c. N = {0,1,2,...}
the set of ...
teori himpunan
{ : }

{ | }
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)}. {nN : n2 <>
the set of ... such that ...
teori himpunan



{}
himpunan kosong ∅ berarti himpunan yang tidak memiliki elemen. {} juga berarti hal yang sama. {nN : 1 < n2 < class="Unicode">∅
himpunan kosong
teori himpunan


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

2−1N
is an element of; is not an element of
everywhere, teori himpunan


subset AB means every element of A is also element of B.

AB means AB but AB.
ABA; QR
is a subset of
teori himpunan


superset AB means every element of B is also element of A.

AB means AB but AB.
ABB; RQ
is a superset of
teori himpunan
set-theoretic union AB means the set that contains all the elements from A and also all those from B, but no others. ABAB = B
the union of ... and ...; union
teori himpunan
set-theoretic intersection AB means the set that contains all those elements that A and B have in common. {xR : x2 = 1} ∩ N = {1}
intersected with; intersect
teori himpunan
\
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
teori himpunan
( )
function application f(x) berarti nilai fungsi f pada elemen x. Jika f(x) := x2, maka f(3) = 32 = 9.
of
teori himpunan
precedence grouping Perform the operations inside the parentheses first. (8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4.
umum
f:XY
function arrow f: XY means the function f maps the set X into the set Y. Let f: ZN be defined by f(x) = x2.
from ... to
teori himpunan
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
teori himpunan

N

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

Z

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

Q

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

π ∉ Q
Q
numbers

R

real numbers R means {limn→∞ an : ∀ nN: anQ, the limit exists}. π ∈ R

√(−1) ∉ R
R
numbers

C

complex numbers C means {a + bi : a,bR}. i = √(−1) ∈ C
C
numbers
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 berarti perbandingan (rasio) antara keliling lingkaran dengan diameternya. A = πr² adalah luas lingkaran dengan jari-jari (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 k=1n ak means a1 + a2 + ... + an. k=14 k2 = 12 + 22 + 32 + 42 = 1 + 4 + 9 + 16 = 30
sum over ... from ... to ... of
aritmatika
product k=1n ak means a1a2···an. k=14 (k + 2) = (1 + 2)(2 + 2)(3 + 2)(4 + 2) = 3 × 4 × 5 × 6 = 360
product over ... from ... to ... of
aritmatika
Cartesian product i=0nYi means the set of all (n+1)-tuples (y0,...,yn). n=13R = Rn
the Cartesian product of; the direct product of
set theory
'
derivative f '(x) is the derivative of the function f at the point x, i.e., the slope of the tangent there. If f(x) = x2, then f '(x) = 2x
… prime; derivative of …
kalkulus
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 …
kalkulus
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
kalkulus
gradient f (x1, …, xn) is the vector of partial derivatives (df / dx1, …, df / dxn). If f (x,y,z) = 3xy + z² then ∇f = (3y, 3x, 2z)
del, nabla, gradient of
kalkulus
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
kalkulus
boundary M means the boundary of M ∂{x : ||x|| ≤ 2} =
{x : || x || = 2}
boundary of
topology
perpendicular xy means x is perpendicular to y; or more generally x is orthogonal to y. If lm and mn then l || n.
is perpendicular to
geometri
bottom element x = ⊥ means x is the smallest element. x : x ∧ ⊥ = ⊥
the bottom element
lattice theory
|=
entailment AB means the sentence A entails the sentence B, that is every model in which A is true, B is also true. AA ∨ ¬A
entails
model theory
|-
inference xy means y is derived from x. AB ⊢ ¬B → ¬A
infers or is derived from
propositional logic, predicate logic
normal subgroup NG 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
isomorphism GH 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

[sumber: wikipedia]

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