Simbolmatematikadasar.docx

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<4 x > y means x lebih besar

5>4

dari y.

order theory

≤

Ketidaksamaan

x ≤ y berarti x lebih kecil dari

3 ≤ 4 and 5 ≤ 5

atau sama dengan y.

≥

5 ≥ 4 and 5 ≥ 5

lebih kecil dari atau sama dengan,

x ≥ y berarti x lebih besar dari

lebih besar dari

atau sama dengan y.

atau sama dengan

order theory

Perjumlahan

tambah

4 + 6 berarti jumlah antara 4 dan 6.

2+7=9

aritmatika

+ disjoint union A1={1,2,3,4} ∧ A2={2,4,5,7} ⇒ the disjoint union of … and …

A1 + A2 means the disjoint

A1 + A2 = {(1,1),

union of sets A1 and A2.

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

aritmatika

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

mempunyai semua anggota

{1,2,4} − {1,3,4} = {

dari Ayang tidak terdapat

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

{1,2} × {3,4} =

product of … and

element of each pair selected

{(1,3),(1,4),(2,3),(2,4

from X and the second

)}

…; the direct product of … and

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)

vector algebra

÷

division bagi

6 ÷ 3 atau 6/3 berati 6 dibagi 3.

/ √

aritmatika square root

2 ÷ 4 = .5 12/4 = 3

√x berarti bilangan positif yang √4 = 2

akar kuadrat

kuadratnya x.

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

X ~ N(0,1),

variable X has the probability

the standard normal

distribution D.

distribution

statistika material implication A ⇒ B means if A is true

⇒

implies; if .. then

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 propositional logic

⊃

forfunctions given below. ⊃ may mean the same as ⇒,

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

or it may have the meaning forsuperset given below.

⇔ ↔ ¬

material equivalence if and only if; iff

A ⇔ B means A is true if B is

x + 5 = y +2 ⇔ x +

true and A is false if B is false.

3=y

propositional logic logical negation

The statement ¬A is true if and ¬(¬A) ⇔ A

not

˜

only if A is false.

x ≠ y ⇔ ¬(x = y)

A slash placed through 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.

propositional

n< 4 ∧ n >2 ⇔ n = 3 when n is anatural number.

logic, lattice theory logical

n≥4 ∨ n≤

disjunction or join i

2 ⇔ n ≠ 3 when n is

n alattice

∨

propositional logic, lattice theory

The statement A ∨ B is true

anatural number.

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

\ The statement A ⊕

⊕

xor

B is true when either A or B,

proposition al logic, Bool ean

but not both,

⊻

are true. A ⊻ B me

||exclusive or

ans the same.

algebra 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

∃

quantification there exists

∃ x: P(x) means there is at least one x such that P(x) is

∃ n ∈ N: n is even.

true.

predicate logic uniqueness

∃!

quantification

∃! x: P(x) means there is

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

∃! n ∈ N: n + 5 = 2n.

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

predicate logic

:=

x := y or x ≡ y means x is

definition is defined as

≡

defined to be another name

cosh x :=

for y (but note that ≡ can also

(1/2)(exp x +

mean other things, such

exp (−x))

as congruence). everywhere

A XOR B :⇔ P :⇔ Q means P is defined to

:⇔

(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

∅ berarti himpunan yang tidak memiliki elemen. {} juga berarti

{} ∈

teori himpunan

4} = ∅

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

∉

hal yang sama.

{n ∈ N : 1 < n2 <

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

⊂ ⊇

∪

of A is also element of B.

A ∩ B ⊆ A; Q ⊂ R

teori himpunan A ⊂ B means A ⊆ B but A ≠ B. superset is a superset of

⊃

A ⊆ B means every element

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

A ∪ B ⊇ B; R ⊃ Q

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

A ∪ B means the set that

the union of ... and contains all the elements

A⊆B ⇔ A∪B=B

...; union teori himpunan

from A and also all those 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 A \ B means the set that

complement

\

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 berarti {0,1,2,3,...}, but see

N

ℕ

the article on natural numbers Bilangan

{|a| : a ∈ Z} = N

for a different convention.

Bilangan bulat

Z

Z

Z berarti {...,−3,−2,−1,0,1,2,3,...}.

ℤ

Bilangan

{a : |a| ∈ N} = Z

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 ∞ is an element of

infinity

∞

infinity numbers pi

is greater than all real

pi Euclidean geometry norm

limx→0 1/|x| = ∞

numbers; it often occurs in limits. π berarti perbandingan (rasio)

π

|| ||

the extended number line that

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

||x+y|| ≤ ||x|| + ||y||

space.

summation

∑

sum over ... from ... to ... of

∑k=1n ak means a1 + a2 + ... + an.

∑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 Cartesian product

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

∏i=0nYi means the set of

∏n=13R = Rn

the Cartesian

all (n+1)-tuples (y0,...,yn).

product of; the direct product of 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 integral from ... to ... of ... with respect to kalkulus

∫ab f(x) dx means the signed area between the xaxis and thegraph of

∫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 derivative of f with respect to

If f(x,y) = x2y, then

xi, with all other variables kept

∂f/∂x = 2xy

kalkulus constant. boundary boundary of

∂M means the boundary of M

∂{x : ||x|| ≤ 2} = {x : || x || = 2}

topology perpendicular

⊥

x ⊥ y means x is perpendicular

is perpendicular to to y; or more generally x is geometri

orthogonal to y.

If l⊥m and m⊥n then 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.

G ≈ H means that group G is is isomorphic to

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

isomorphism

≈

{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