Tabel lambang matematis

Matematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. Pikeun nu icikibung dina widang matematik mah, moal kukumaha, tapi pikeun nu arang nempo, sigana kudu mindeng ngapalkeun. Di handap ieu dibéréndélkeun rupa-rupa lambang matematis katut ngarana, éjahanana, jeung saeutik dadaranana.

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Lambang	Ngaran	Dibaca	Kategori
+	tambah	plus	aritmétik
	4 + 6 = 10 nu hartina mun opat ditambahkeun ka genep, jumlahna, atawa hasilna, nyéta 10.
	43 + 65 = 108; 2 + 7 = 9
−	kurang	minus	aritmétik
	9 − 4 = 5 nu hartina mun salapan dikurangan opat, hasilna bakal lima. Tanda minus ogé nandakeun yén hiji angka négatif. Pikeun conto, 5 + (−3) = 2 hartina mun lima ditambahkeun jeung négatif tilu, hasilna dua.
	36 − 5 = 31
⇒ →	material implication	implies; if .. then	propositional logic
	A ⇒ B méans: if A is true then B is also true; if A is false then nothing is said about B. → may méan the same as ⇒, or it may have the méaning for functions mentioned further down
	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	propositional logic
	A ⇔ B méans: A is true if B is true and A is false if B is false
	x + 5 = y + 2  ⇔  x + 3 = y
∧	logical conjunction or meet in a lattice	and	propositional logic, lattice theory
	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
∨	logical disjunction or join in a lattice	or	propositional logic, lattice theory
	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
¬ /	logical negation	not	propositional logic
	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 ∧ B) ⇔ (¬A) ∨ (¬B); x ∉ S  ⇔  ¬(x ∈ S)
∀	universal quantification	for all; for any; for éach	predicate logic
	∀ x: P(x) méans: P(x) is true for all x
	∀ n ∈ N: n2 ≥ n
∃	existential quantification	there exists	predicate logic
	∃ x: P(x) méans: there is at léast one x such that P(x) is true
	∃ n ∈ N: n + 5 = 2n
=	equality	equals	everywhere
	x = y méans: x and y are different names for precisely the same thing
	1 + 2 = 6 − 3
:= ≡ :⇔	definition	is defined as	everywhere
	x := y or x ≡ y méans: x is defined to be another name for y (but note that ≡ can also méan other things, such as congruence) P :⇔ Q méans: P is defined to be logically equivalent to Q
	cosh x := (1/2)(exp x + exp (−x)); A XOR B :⇔ (A ∨ B) ∧ ¬(A ∧ B)
{ , }	set brackets	the set of ...	set theory
	{a,b,c} méans: the set consisting of a, b, and c
	N = {0,1,2,...}
{ : } { | }	set builder notation	the set of ... such that ...	set theory
	{x : P(x)} méans: 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}
∅ {}	empty set	empty set	set theory
	{} méans: the set with no elements; ∅ is the same thing
	{n ∈ N : 1 < n2 < 4} = {}
∈ ∉	set membership	in; is in; is an element of; is a member of; belongs to	set theory
	a ∈ S méans: a is an element of the set S; a ∉ S méans: a is not an element of S
	(1/2)−1 ∈ N; 2−1 ∉ N
⊆ ⊂	subset	is a subset of	set theory
	A ⊆ B méans: every element of A is also element of B A ⊂ B méans: A ⊆ B but A ≠ B
	A ∩ B ⊆ A; Q ⊂ R
∪	set theoretic union	the union of ... and ...; union	set theory
	A ∪ B méans: the set that contains all the elements from A and also all those from B, but no others
	A ⊆ B  ⇔  A ∪ B = B
∩	set theoretic intersection	intersected with; intersect	set theory
	A ∩ B méans: the set that contains all those elements that A and B have in common
	{x ∈ R : x2 = 1} ∩ N = {1}
\	set theoretic complement	minus; without	set theory
	A \ B méans: the set that contains all those elements of A that are not in B
	{1,2,3,4} \ {3,4,5,6} = {1,2}
( ) [ ] { }	function application; grouping	of	set theory
	for function application: f(x) méans: the value of the function f at the element x for grouping: perform the operations inside the parentheses first
	If f(x) := x2, then f(3) = 32 = 9; (8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4
f:X→Y	function arrow	from ... to	functions
	f: X → Y méans: the function f maps the set X into the set Y
	Consider the function f: Z → N defined by f(x) = x2
N	natural numbers	N	numbers
	N méans {0,1,2,3,...}, but see the article on natural numbers for a different convention.
	{|a| : a ∈ Z} = N
Z	integers	Z	numbers
	Z méans: {...,−3,−2,−1,0,1,2,3,...}
	{a : |a| ∈ N} = Z
Q	rational numbers	Q	numbers
	Q méans: {p/q : p,q ∈ Z, q ≠ 0}
	3.14 ∈ Q; π ∉ Q
R	real numbers	R	numbers
	R méans: {limn→∞ an : ∀ n ∈ N: an ∈ Q, the limit exists}
	π ∈ R; √(−1) ∉ R
C	complex numbers	C	numbers
	C méans: {a + bi : a,b ∈ R}
	i = √(−1) ∈ C
< >	comparison	is less than, is gréater than	partial orders
	x < y méans: x is less than y; x > y méans: x is gréater than y
	x < y  ⇔  y > x
≤ ≥	comparison	is less than or equal to, is gréater than or equal to	partial orders
	x ≤ y méans: x is less than or equal to y; x ≥ y méans: x is gréater than or equal to y
	x ≥ 1  ⇒  x2 ≥ x
√	square root	the principal square root of; square root	real numbers
	√x méans: the positive number whose square is x
	√(x2) = |x|
∞	infinity	infinity	numbers
	∞ is an element of the extended number line that is gréater than all réal numbers; it often occurs in limits
	limx→0 1/|x| = ∞
π	pi	pi	Euclidean geometry
	π méans: the ratio of a circle's circumference to its diaméter
	A = πr² is the aréa of a circle with radius r
!	factorial	factorial	combinatorics
	n! is the product 1×2×...×n
	4! = 24
| |	absolute value	absolute value of	numbers
	|x| méans: the distance in the real line (or the complex plane) between x and zero
	|a + bi| = √(a2 + b2)
|| ||	norm	norm of; length of	functional analysis
	||x|| is the norm of the element x of a normed vector space
	||x+y|| ≤ ||x|| + ||y||
∑	summation	sum over ... from ... to ... of	arithmetic
	∑k=1n ak méans: a1 + a2 + ... + an
	∑k=14 k2 = 12 + 22 + 32 + 42 = 1 + 4 + 9 + 16 = 30
∏	product	product over ... from ... to ... of	arithmetic
	∏k=1n ak méans: a1a2···an
	∏k=14 (k + 2) = (1  + 2)(2 + 2)(3 + 2)(4 + 2) = 3 × 4 × 5 × 6 = 360
∫	integration	integral from ... to ... of ... with respect to	calculus
	∫ab f(x) dx méans: 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; ∫x2 dx = x3/3
f '	derivative	derivative of f; f prime	calculus
	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 and f ''(x) = 2
∇	gradient	del, nabla, gradient of	calculus
	∇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) A transparent image for text is: Image:Del.svg ().
∂	partial	partial derivative of	calculus
	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
⊥	perpendicular	is perpendicular to	orthogonality
	x ⊥ y méans: x is perpendicular to y; or more generally x is orthogonal to y.
⊥	bottom element	the bottom element	lattice theory
	x = ⊥ méans: x is the smallest element.
	insert more (suggestions are the inequality symbols); some symbols are used in examples before they are defined

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Tumbu kaluar

• Jeff Miller: éarliest Uses of Various Mathematical Symbols, https://web.archive.org/web/20081204035420/http://members.aol.com/jeff570/mathsym.html
• TCAEP - Institute of Physics, http://www.tcaep.co.uk/science/symbols/maths.htm Archived 2004-08-29 di Wayback Machine