Tabel lambang matematis

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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

&minus;
kurang
minus
aritmétik
 9 &minus; 4 = 5 nu hartina mun salapan dikurangan opat, hasilna bakal lima. Tanda minus ogé nandakeun yén hiji angka négatif. Pikeun conto, 5 + (&minus;3) = 2 hartina mun lima ditambahkeun jeung négatif tilu, hasilna dua. 36 &minus; 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&nbsp;&nbsp;⇒&nbsp; *x*2 = 4 is true, but *x*2 = 4 &nbsp;&nbsp;⇒&nbsp; *x* = 2 is in general false (since *x* could be &minus;2)

 
  ⇔↔
  material equivalence
  if and only if; iff
  propositional logic
  *A*&nbsp;⇔ *B* méans: *A* is true if *B* is true and *A* is false if *B* is false
  *x*&nbsp;+ 5&nbsp;= *y*&nbsp;+ 2&nbsp;&nbsp;⇔&nbsp; *x*&nbsp;+ 3&nbsp;= *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*&nbsp; 2&nbsp;&nbsp;⇔&nbsp; *n*&nbsp;= 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*&nbsp;≥ 4&nbsp;&nbsp;∨&nbsp; *n*&nbsp;≤ 2&nbsp;&nbsp;⇔ *n*&nbsp;≠ 3 when n is a natural number

 
  ¬/
  logical negation
  not
  propositional logic
  the statement ¬*A* is true if and only if *A* is falsea slash placed through another operator is the same as "&not;" placed in front
  ¬(*A*&nbsp;∧ *B*)&nbsp;⇔ (¬*A*)&nbsp;∨ (¬*B*); x&nbsp;∉ S&nbsp;&nbsp;⇔&nbsp; ¬(x&nbsp;∈ S)

 
  ∀
  universal quantification
  for all; for any; for éach
  predicate logic
  ∀&nbsp;*x*: *P*(*x*) méans: *P*(*x*) is true for all *x*
  ∀&nbsp;*n*&nbsp;∈ **N**: *n*2&nbsp;≥ *n*

 
  ∃
  existential quantification
  there exists
  predicate logic
  ∃&nbsp;*x*: *P*(*x*) méans: there is at léast one *x* such that *P*(*x*) is true
  ∃&nbsp;*n*&nbsp;∈ **N**: *n*&nbsp;+ 5&nbsp;= 2*n*

 
  =
  equality
  equals
  everywhere
  x&nbsp;= y méans: x and y are different names for precisely the same thing
  1&nbsp;+ 2&nbsp;= 6&nbsp;&minus; 3

 
  :=≡:⇔
  definition
  is defined as
  everywhere
  x&nbsp;:= y or x&nbsp;≡ y méans: x is defined to be another name for y (but note that ≡ can also méan other things, such as congruence)P&nbsp;:⇔ Q méans: P is defined to be logically equivalent to Q
  cosh&nbsp;*x*&nbsp;:= (1/2)(exp&nbsp;*x*&nbsp;+ exp&nbsp;(&minus;*x*)); *A* XOR *B*&nbsp;:⇔ (*A*&nbsp;∨ *B*)&nbsp;∧ ¬(*A*&nbsp;∧ *B*)

 
  { , }
  set brackets
  the set of ...
  set theory
  {a,b,c} méans: the set consisting of a, b, and c
  **N**&nbsp;= {0,1,2,...}

 
  { : }{ | }
  set builder notation
  the set of ... such that ...
  set theory
  {*x*&nbsp;: *P*(*x*)} méans: the set of all *x* for which *P*(*x*) is true. {*x*&nbsp;| *P*(*x*)} is the same as {*x*&nbsp;: *P*(*x*)}.
  {*n*&nbsp;∈ **N**&nbsp;: *n*2&nbsp;
  ∅{}
  empty set
  empty set
  set theory
  {} méans: the set with no elements; ∅ is the same thing
  {*n*&nbsp;∈ **N**&nbsp;: 1&nbsp;2&nbsp;
  ∈∉
  set membership
  in; is in; is an element of; is a member of; belongs to
  set theory
  *a*&nbsp;∈ *S* méans: *a* is an element of the set *S*; *a*&nbsp;∉ *S* méans: *a* is not an element of *S*
  (1/2)&minus;1&nbsp;∈ **N**; 2&minus;1&nbsp;∉ **N**

 
  ⊆⊂
  subset
  is a subset of
  set theory
  *A*&nbsp;⊆ *B* méans: every element of *A* is also element of *B**A*&nbsp;⊂ *B* méans: A&nbsp;⊆ B but *A*&nbsp;≠ *B*
  *A*&nbsp;∩ *B* ⊆ *A*; **Q**&nbsp;⊂ **R**

 
  ∪
  set theoretic union
  the union of ... and ...; union
  set theory
  *A*&nbsp;∪ *B* méans: the set that contains all the elements from *A* and also all those from *B*, but no others
  *A*&nbsp;⊆ *B*&nbsp;&nbsp;⇔&nbsp; *A*&nbsp;∪ *B*&nbsp;= *B*

 
  ∩
  set theoretic intersection
  intersected with; intersect
  set theory
  *A*&nbsp;∩ *B* méans: the set that contains all those elements that *A* and *B* have in common
  {*x*&nbsp;∈ **R**&nbsp;: *x*2&nbsp;= 1}&nbsp;∩ **N**&nbsp;= {1}

 
  \
  set theoretic complement
  minus; without
  set theory
  *A*&nbsp;\ *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 xfor grouping: perform the operations inside the parentheses first
  If f(x)&nbsp;:= x2, then f(3)&nbsp;= 32&nbsp;= 9; (8/4)/2&nbsp;= 2/2&nbsp;= 1, but 8/(4/2)&nbsp;= 8/2&nbsp;= 4

 
  *f*:*X*→*Y*
  function arrow
  from ... to
  functions
  f:&nbsp;X&nbsp;→ Y méans: the function f maps the set X into the set Y
  Consider the function f:&nbsp;**Z**&nbsp;→ **N** defined by f(x)&nbsp;= x2

 
  N
  natural numbers
  N
  numbers
  **N** méans {0,1,2,3,...}, but see the article on natural numbers for a different convention.
  {|*a*|&nbsp;: *a*&nbsp;∈ **Z**}&nbsp;= **N**

 
  Z
  integers
  Z
  numbers
  **Z** méans: {...,&minus;3,&minus;2,&minus;1,0,1,2,3,...}
  {*a*&nbsp;: |*a*|&nbsp;∈ **N**}&nbsp;= **Z**

 
  Q
  rational numbers
  Q
  numbers
  **Q** méans: {*p*/*q*&nbsp;: *p*,*q*&nbsp;∈ **Z**, *q*&nbsp;≠ 0}
  3.14&nbsp;∈ **Q**; π&nbsp;∉ **Q**

 
  R
  real numbers
  R
  numbers
  **R** méans: {limn→∞&nbsp;*a**n*&nbsp;: ∀&nbsp;*n*&nbsp;∈ **N**: a*n*&nbsp;∈ **Q**, the limit exists}
  π&nbsp;∈ **R**; √(&minus;1)&nbsp;∉ **R**

 
  C
  complex numbers
  C
  numbers
  **C** méans: {*a*&nbsp;+ *bi*&nbsp;: *a*,*b*&nbsp;∈ **R**}
  *i*&nbsp;= √(&minus;1)&nbsp;∈ **C**

 
  &lt;&gt;
  comparison
  is less than, is gréater than
  partial orders
  *x*&nbsp;&lt; *y* méans: *x* is less than *y*; *x*&nbsp;> *y* méans: *x* is gréater than *y*
  *x*&nbsp;&lt; *y*&nbsp;&nbsp;⇔&nbsp; y&nbsp;&gt; x

 
  ≤≥
  comparison
  is less than or equal to, is gréater than or equal to
  partial orders
  x&nbsp;≤ y méans: x is less than or equal to y; *x*&nbsp;≥ *y* méans: *x* is gréater than or equal to *y*
  *x*&nbsp;≥ 1&nbsp;&nbsp;⇒&nbsp; *x*2&nbsp;≥ *x*

 
  √
  square root
  the principal square root of; square root
  real numbers
  √*x* méans: the positive number whose square is *x*
  √(*x*2)&nbsp;= |*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&nbsp;1/|*x*|&nbsp;= ∞

 
  π
  pi
  pi
  Euclidean geometry
  π méans: the ratio of a circle's circumference to its diaméter
  *A*&nbsp;= π*r*² is the aréa of a circle with radius *r*

 
  !
  factorial
  factorial
  combinatorics
  *n*! is the product 1&times;2&times;...&times;*n*
  4! = 24

 
  |&nbsp;|
  absolute value
  absolute value of
  numbers
  |x| méans: the distance in the real line (or the complex plane) between x and zero
  |*a*&nbsp;+ *bi*|&nbsp;= √(*a*2&nbsp;+ *b*2)

 
  ||&nbsp;||
  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*=1*n*&nbsp;*a**k* méans: *a*1&nbsp;+ *a*2&nbsp;+ ...&nbsp;+ *a**n*
  ∑*k*=14&nbsp;*k*2&nbsp;= 12&nbsp;+ 22&nbsp;+ 32&nbsp;+ 42&nbsp;= 1&nbsp;+ 4&nbsp;+ 9&nbsp;+ 16&nbsp;= 30

 
  ∏
  product
  product over ... from ... to ... of
  arithmetic
  ∏*k*=1*n*&nbsp;*a**k* méans: *a*1*a*2···*a**n*
  ∏*k*=14&nbsp;(*k*&nbsp;+ 2)&nbsp;= (1&nbsp; + 2)(2&nbsp;+ 2)(3&nbsp;+ 2)(4&nbsp;+ 2)&nbsp;= 3&nbsp;&times; 4&nbsp;&times; 5&nbsp;&times; 6&nbsp;= 360

 
  ∫
  integration
  integral from ... to ... of ... with respect to
  calculus
  ∫*a**b*&nbsp;*f*(*x*)&nbsp;d*x* méans: the signed area between the *x*-axis and the graph of the function *f* between x&nbsp;= *a* and x&nbsp;= *b*
  ∫0*b*&nbsp;x2&nbsp;d*x*&nbsp;= *b*3/3; ∫*x*2&nbsp;d*x*&nbsp;= *x*3/3

 
  *f*&nbsp;'
  derivative
  derivative of f; f prime
  calculus
  *f*&nbsp;'(*x*) is the derivative of the function *f* at the point *x*, i.e., the slope of the tangent there
  If *f*(*x*) = *x*2, then *f*&nbsp;'(*x*) = 2*x* and *f*&nbsp;'&apos;(*x*) = 2

 
  ∇
  gradient
  del, nabla, gradient of
  calculus
  ∇*f* (x1, …, x*n*) is the vector of partial derivatives (*df* / *dx*1, …, *df* / *dx**n*)
  If *f* (*x*,*y*,*z*) = 3*xy* + *z*² then ∇*f* = (3*y*, 3*x*, 2*z*)
A transparent image for text is: Image:Del.svg ().

 
  ∂
  partial
  partial derivative of
  calculus
   With *f* (x1, …, x*n*), ∂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