Simbol matematika dasar

Simbol matematika dasar
Nama

Simbol

Dibaca sebagai

Penjelasan

Contoh

Kategori

Kesamaan

=

sama dengan

x = y berarti x and y mewakili
hal atau nilai yang sama.

1+1=2

umum

Ketidaksamaan

≠

x ≠ y berarti x dan y tidak
tidak sama dengan mewakili hal atau nilai yang

1≠2

sama.
umum

Ketidaksamaan

<

x < y berarti x lebih kecil dari y.
lebih kecil dari;

>

lebih besar dari

3 y means x lebih besar

5>4

dari y.
order theory

≤

Ketidaksamaan

x ≤ y berarti x lebih kecil dari

3 ≤ 4 and 5 ≤ 5

lebih kecil dari atau
sama dengan,
lebih besar dari

≥

atau sama dengan

atau sama dengan y.
x ≥ y berarti x lebih besar dari

5 ≥ 4 and 5 ≥ 5

atau sama dengan y.
order theory

Perjumlahan

tambah

4 + 6 berarti jumlah antara 4
dan 6.

2+7=9

aritmatika

+
disjoint union

the disjoint union
of … and …

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)}

teori himpunan

−

Perkurangan

kurang

9 − 4 berarti 9 dikurangi 4.

8−3=5

aritmatika

tanda negatif

negatif

−3 berarti negatif dari angka 3. −(−5) = 5

aritmatika

set-theoretic
complement
A − B berarti himpunan yang
mempunyai semua anggota
minus; without

dari Ayang tidak terdapat

{1,2,4} − {1,3,4} = {2}

pada B.
set theory

multiplication

kali

3 × 4 berarti perkalian 3 oleh
4.

7 × 8 = 56

aritmatika

×

Cartesian product
X×Y means the set of
the Cartesian

all ordered pairs with the first

product of … and

element of each pair selected

…; the direct
product of … and

{1,2} × {3,4} = {(1,3),(1,4),(2,3),(2,4)}

from X and the second
element selected from Y.

…
teori himpunan
cross product
cross

u × v means the cross

(1,2,5) × (3,4,−1) =

product of vectors u and v

(−22, 16, − 2)

6 ÷ 3 atau 6/3 berati 6 dibagi

2 ÷ 4 = .5

vector algebra

÷

division
bagi

3.

aritmatika
12/4 = 3
square root
akar kuadrat

√x berarti bilangan positif yang
kuadratnya x.

√4 = 2

bilangan real

√

complex square
root
the complex
square root of;
square root

if z = r exp(iφ) is represented
in polar coordinates with -π <

√(-1) = i

φ ≤ π, then √z = √r exp(iφ/2).

Bilangan kompleks
absolute value

||

nilai mutlak dari
numbers

|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

factorial

!

faktorial

n! adalah hasil dari 1×2×...×n.

4! = 1 × 2 × 3 × 4 = 24

combinatorics
probability
distribution

~

has distribution;
tidk terhingga

X ~ D, means the random
variable X has the probability

X ~ N(0,1), the standard normal distribution

distribution D.

statistika
material implication A ⇒ B means if A is true

⇒

implies; if .. then

then nothing is said about B.
→ may mean the same as ⇒,

→

or it may have the meaning
propositional logic

⊃

then B is also true; if A is false

forfunctions given below.
⊃ may mean the same as ⇒,
or it may have the meaning
forsuperset given below.

x = 2 ⇒ x2 = 4 is true, but x2 = 4 ⇒ x= 2 is in
general false (since x could be −2).

⇔

material
equivalence
if and only if; iff

↔

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

propositional logic
logical negation

¬

not

The statement ¬A is true if and
only if A is false.
¬(¬A) ⇔ A
A slash placed through

˜

x ≠ y ⇔ ¬(x = y)

propositional logic another operator is the same
as "¬" placed in front.
logical
conjunction or mee
t in alattice

∧

and

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 anatural
number.

propositional
logic, lattice theory
logical
disjunction or join i
n alattice

∨

n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is anatural number.
The statement A ∨ B is true

if A or B (or both) are true; if
propositional both are false, the statement is \

logic, lattice theory false.
The
statement A ⊕

⊕

xor

B is true when

proposition

either A or B,

al

but not both,

logic, Bool
ean
algebra

⊻

are
true. A ⊻ B me

||exclusive or

ans the same.

universal
quantification

∀

for all; for any; for
each

∀ x: P(x) means P(x) is true for
all x.

∀ n ∈ N: n2 ≥ n.

predicate logic

∃

existential

∃ x: P(x) means there is at

quantification

least one x such that P(x) is

there exists

true.

∃ n ∈ N: n is even.

(¬A)
⊕ A is
always
true, A ⊕
A is
always
false.

predicate logic
uniqueness
quantification

∃!

∃! x: P(x) means there is

there exists exactly exactly one x such that P(x) is
one

∃! n ∈ N: n + 5 = 2n.

true.

predicate logic

:=

definition

x := y or x ≡ y means x is

is defined as

≡

defined to be another name
for y (but note that ≡ can also
mean other things, such
as congruence).

everywhere

:⇔

P :⇔ Q means P is defined to

cosh x := (1/2)
(exp x + exp (−x))
A XOR B :⇔
(A ∨ B) ∧ ¬(A ∧ B)

be logically equivalent to Q.
set brackets

{,}

the set of ...

{a,b,c} means the set
consisting of a, b, and c.

N = {0,1,2,...}

teori himpunan

{:}

set builder notation
the set of ... such

{|}

that ...
teori himpunan

{x : P(x)} means the set of
all x for which P(x) is true.

{n ∈ N : n2 < 20} =

{x | P(x)} is the same as

{0,1,2,3,4}

{x : P(x)}.

himpunan kosong

∅
{}
∈

himpunan kosong
teori himpunan

memiliki elemen. {} juga berarti
hal yang sama.

{n ∈ N : 1 < n2 <
4} = ∅

set membership
is an element of; is a ∈ S means a is an element
not an element of

∉

∅ berarti himpunan yang tidak

everywhere, teori

(1/2)−1 ∈ N

of the set S; a ∉ S means a is
not an element of S.

2−1 ∉ N

himpunan

⊆

subset
is a subset of

⊂

A ⊆ B means every element
of A is also element of B.

teori himpunan A ⊂ B means A ⊆ B but A ≠ B.

A ∩ B ⊆ A; Q ⊂ R

⊇

superset

A ⊇ B means every element

is a superset of

⊃

A ∪ B ⊇ B; R ⊃ Q

teori himpunan A ⊃ B means A ⊇ B but A ≠ B.
set-theoretic union

∪

of B is also element of A.

A ∪ B means the set that

the union of ...

contains all the elements

and ...; union

from A and also all those

teori himpunan

A⊆B ⇔ A∪B=B

from B, but no others.

set-theoretic
intersection

∩

A ∩ B means the set that

intersected with;
intersect

contains all those elements
that A andB have in common.

{x ∈ R : x2 =
1} ∩ N = {1}

teori himpunan
set-theoretic

\

complement

A \ B means the set that

minus; without

contains all those elements
of A that are not in B.

{1,2,3,4} \ {3,4,5,6} =
{1,2}

teori himpunan
function application
of

()

f(x) berarti nilai fungsi f pada

Jika f(x) := x2,

elemen x.

maka f(3) = 32 = 9.

Perform the operations inside

(8/4)/2 = 2/2 = 1, but

the parentheses first.

8/(4/2) = 8/2 = 4.

teori himpunan
precedence
grouping
umum

f:X→
Y

function arrow
from ... to
teori himpunan

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.

function
composition

o

composed with

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).

teori himpunan
Bilangan asli

N

N

N berarti {0,1,2,3,...}, but see
the article on natural numbers

{|a| : a ∈ Z} = N

Bilangan
for a different convention.

ℕ
Z

Bilangan bulat
Z berarti {...,

Z

−3,−2,−1,0,1,2,3,...}.

ℤ

{a : |a| ∈ N} = Z

Bilangan
Bilangan rasional

Q

3.14 ∈ Q

Q

ℚ

Q berarti {p/q : p,q ∈ Z, q ≠ 0}.
π∉Q

Bilangan
Bilangan real

R

R berarti {limn→∞ an :

R

ℝ

π∈R

∀ n ∈ N: an ∈ Q, the limit
Bilangan

exists}.

√(−1) ∉ R

C means {a + bi : a,b ∈ R}.

i = √(−1) ∈ C

Bilangan kompleks

C

C

ℂ

Bilangan
infinity

∞

∞ is an element of
infinity
numbers

pi

is greater than all real

Euclidean
geometry
norm

in limits.

antara
keliling lingkaran dengan
diameternya.

A = πr² adalah luas
lingkaran dengan
jari-jari (radius) r

||x|| is the norm of the

norm of; length of
linear algebra

element x of a normed vector

∑k=1n ak means a1 + a2 + ... + an
sum over ...
from ... to ... of

||x+y|| ≤ ||x|| + ||y||

space.

summation

∑

limx→0 1/|x| = ∞

numbers; it often occurs

π berarti perbandingan (rasio)
pi

π

|| ||

the extended number line that

.

∑k=14 k2 = 12 + 22 +
32 + 42 = 1 + 4 + 9 +
16 = 30

aritmatika
product

∏k=14 (k + 2) = (1 +

product over ...
from ... to ... of

∏k=1n ak means a1a2···an.

2) = 3 × 4 × 5 × 6 =
360

aritmatika

∏

2)(2 + 2)(3 + 2)(4 +

Cartesian product
the Cartesian
product of; the
direct product of

∏i=0nYi means the set of
all (n+1)-tuples (y0,...,yn).

∏n=13R = Rn

set theory
derivative

'

… prime;
derivative of …

f '(x) is the derivative of the
function f at the point x, i.e.,
theslope of the tangent there.

If f(x) = x2,
then f '(x) = 2x

kalkulus
indefinite
integral or antideriv
ative
indefinite integral
of …; the

∫ f(x) dx means a function
whose derivative is f.

∫x2 dx = x3/3 + C

antiderivative of …

∫

kalkulus
definite integral

∫ab f(x) dx means the

integral from ...

signed area between the x-

to ... of ... with

axis and thegraph of

respect to
kalkulus

∫0b x2 dx = b3/3;

the function f between x = a an
d x = b.

gradient

∇

del, nabla, gradient
of

∇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)

kalkulus

∂

partial derivative
partial derivative of

With f (x1, …, xn), ∂f/∂xi is the

If f(x,y) = x2y, then

derivative of f with respect to

∂f/∂x = 2xy

xi, with all other variables kept

kalkulus constant.

boundary
boundary of

∂M means the boundary of M

∂{x : ||x|| ≤ 2} =
{x : || x || = 2}

topology
perpendicular

x ⊥ y means x is

is perpendicular to perpendicular to y; or more

⊥

geometri

generally x is orthogonal to y.

If l⊥m and m⊥n the
n l || n.

bottom element
the bottom element

x = ⊥ means x is the smallest
element.

∀x : x ∧ ⊥ = ⊥

lattice theory
A ⊧ B means the

entailment

|=

sentence A entails the

entails

sentence B, that is

model theory

A ⊧ A ∨ ¬A

everymodel in which A is
true, B is also true.

inference
infers or is derived

|-

x ⊢ y means y is derived

from
propositional

from x.

A → B ⊢ ¬B → ¬A

logic, predicate
logic
normal subgroup

◅

is a normal

N ◅ G means that N is a

subgroup of

normal subgroup of group G.

Z(G) ◅ G

group theory
quotient group

/

mod
group theory

G/H means the quotient of
group G modulo its
subgroup H.

isomorphism

≈

2a, b, b+a, b+2a} /
{0, b} = {{0, b},
{a, b+a}, {2a, b+2a}}
Q / {1, −1} ≈ V,

G ≈ H means that group G is
is isomorphic to

{0, a,

isomorphic to group H

where Q is
the quaternion
group and V is
the Klein four-group.

Istilah Matematika Dalam Bahasa Inggris
Berikut beberapa istilah-istilah matematika dalam bahasa Inggris.


Bilangan Bulat = Integers (Z)



Bilangan Asli = Natural number (N)



Bilangan Cacah = Whole number (W)



Bilangan Genap = Even number



Bilangan Ganjil = Odd number



Penjumlahan = Addition



Pengurangan = Subtraction



Pembagian = Divisio



Perkalian = Multiplication



Sifat asosiatif = Associative principle



Sifat komutatif = Commutative principle



Kelipatan persekutuan terkecil (KPK) = Least common multiple



Faktor persekutuan terbesar (FPB) = Greatest common divisor



Pecahan = fraction



Pecahan-pecahan yang senilai dan tidak senilai = Equality and inequality of
rational numbers



Pecahan campuran = Mixed rational number



Desimal = Decimals



Operasi bilangan desimal = The operations of decimals



Garis bilangan = The number line



Bentuk baku = Scientific notation



Pangkat bilangan = Powers of numbers



Bentuk aljabar = Algebraic forms



Aritmatika sosial = Social arithmetic



Persamaan linier = Linear equations



Variabel = Variable



Pertidaksamaan linier = Linear inequalities



Modulus (Pengayaan) = Enrichment



Perbandingan = Proportion



Pembilang= Numerator



Penyebut = Denominator



Perbandingan seharga = Direct proportion



Perbandingan berbalik harga = Inverse proportion



Garis = Lines



Sudut = Angles



Derajat = Degrees



Keliling = Circumference



Luas = Area



Sisi = Side



Sudut dalam = Interior angle



Himpunan = Sets



Himpunan semesta = Universal set



Gabungan himpunan = Union of sets



Irisan himpunan = Intersection of sets



Komplemen suatu himpunan = Complement of a set



Diagram Venn = Venn diagrams



Himpunan-himpunan yang sama = Equal sets



Himpunan-himpunan yang ekuivalen = Equivalent sets



Himpunan-himpunan yang saling lepas (Saling asing) = Disjoint sets