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 |
x ≠ y 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
5 > 4 |
| lebih kecil dari; lebih besar dari |
| order theory |
≤
≥
|
inequality |
x ≤ y berarti x lebih kecil dari atau sama dengan y.
x ≥ y berarti 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 |
A − B berarti himpunan yang mempunyai semua anggota dari A yang tidak terdapat pada B. |
{1,2,4} − {1,3,4} = {2} |
| minus; without |
| set theory |
×
|
multiplication |
3 × 4 berarti perkalian 3 oleh 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 kompleks |
| |
|
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 |
| nilai mutlak dari |
| numbers |
!
|
factorial |
n! adalah hasil dari 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 |
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. |
n < 4 ∧ n >2 ⇔ n = 3 when n is a natural number. |
| and |
| 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. |
n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number.
\
|
| 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 |
∀
|
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 |
{ , }
|
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)}. |
{n ∈ N : n2 < 20} = {0,1,2,3,4} |
| the set of ... such that ... |
| teori himpunan |
∅
{}
|
himpunan kosong |
∅ berarti himpunan yang tidak memiliki elemen. {} juga berarti hal yang sama. |
{n ∈ N : 1 < n2 < 4} = ∅ |
| himpunan kosong |
| teori himpunan |
∈
∉
|
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, teori himpunan |
⊆
⊂
|
subset |
A ⊆ B means every element of A is also element of B.
A ⊂ B means A ⊆ B but A ≠ B. |
A ∩ B ⊆ A; Q ⊂ R |
| is a subset of |
| teori himpunan |
⊇
⊃
|
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 |
| teori himpunan |
∪
|
set-theoretic union |
A ∪ B means the set that contains all the elements from A and also all those from B, but no others. |
A ⊆ B ⇔ A ∪ B = B |
| the union of ... and ...; union |
| teori himpunan |
∩
|
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 |
| 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: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 |
| 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
ℕ
|
Bilangan asli |
N berarti {0,1,2,3,...}, but see the article on natural numbers for a different convention. |
{|a| : a ∈ Z} = N |
| N |
| Bilangan |
Z
ℤ
|
Bilangan bulat |
Z berarti {...,−3,−2,−1,0,1,2,3,...}. |
{a : |a| ∈ N} = Z |
| Z |
| Bilangan |
Q
ℚ
|
Bilangan rasional |
Q berarti {p/q : p,q ∈ Z, q ≠ 0}. |
3.14 ∈ Q
π ∉ Q |
| Q |
| Bilangan |
R
ℝ
|
Bilangan real |
R berarti {limn→∞ an : ∀ n ∈ N: an ∈ Q, the limit exists}. |
π ∈ R
√(−1) ∉ R |
| R |
| Bilangan |
C
ℂ
|
Bilangan kompleks |
C means {a + bi : a,b ∈ R}. |
i = √(−1) ∈ C |
| C |
| Bilangan |
∞
|
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 |
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 |
| geometri |
| bottom element |
x = ⊥ means x is the smallest element. |
∀x : x ∧ ⊥ = ⊥ |
| the bottom element |
| lattice theory |
|=
|
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 |
≈
|
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 |
