Symbolen verzamelingenleer - 2004

In het dictaat van Quantummechanica voor HOVO van 2004 wordt een aantal wiskundige onderwerpen besproken. Het betreft met name hoofdstuk 1 en 6. Hierbij gelden de volgende afkortingen:

• De lengte of absolute waarde van een vector wordt aangegeven met
  
  $$\vert {\bf a} \vert ~~~~{\rm of}~~~~\Vert {\bf a} \Vert$$
  
  

• Indien ${\bf a}$ een element is van een verzameling $L$, schrijft men
  
  $${\bf a} \in L$$
  
  

• Indien een eigenschap geldt voor alle elementen ${\bf a}$, schrijft men
  
  $$\forall_{\bf a}$$
  
  

• Indien een eigenschap geldt voor alle elementen ${\bf a}$ uit een verzameling $L$, schrijft men
  
  $$\forall_{{\bf a} \in L}$$
  
  

• Indien men stelt dat er een element ${\bf a}$ bestaat, schrijft men
  
  $$\exists_{\bf a}$$
  
  

• Indien men stelt dat er slechts één element ${\bf a}$ bestaat, schrijft men
  
  $$\exists !_{\bf a}$$
  
  

• Indien men stelt dat de verzameling ${\bf A}$ (bijvoorbeeld de getallen $\{ 1,2 \}$) een deelverzameling is van de verzameling der natuurlijke getallen ${\mathbb{N}}$, schrijft men
  
  $${\bf A} \subset {\mathbb{N}}$$
  
  

• Indien men stelt dat de verzameling der natuurlijke getallen ${\mathbb{N}}$, de verzameling ${\bf A}$ (bijvoorbeeld de getallen $\{ 1,2 \}$) omvat, schrijft men
  
  $${\mathbb{N}} \supset {\bf A}$$
  
  

Mathematische Symbolen

Deze tabel bevat mathematische symbolen en definities van wat ze betekenen.

Note: laden van deze pagina kan enige tijd vergen. Verder sorry voor het Engels...

Symbol	What it is	How it is read	How it is used	Sample expression
+	Addition sign Logical OR symbol	... plus ... ... or ...	Sum of a few values Logical disjunction	3 + 5 = 8 ¬(A + B) = ¬A * ¬B
*	Multiplication sign Logical AND symbol	... times ... ... and ...	Product of two values Logical conjunction	3 x 5 = 15 ¬(A * B) = ¬A + ¬B
x	Multiplication sign	... times ...	Product of two values	3 x 5 = 15
·	Multiplication sign	... times ...	Product of two values	3 · 5 = 15
	summation sign	The summation of ...	Sum of many or infinitely many values
	Integral sign	The integral of ...	integration	x2 dx = x3/3 + c
	double integral sign	The double integral of ...	integration	f(x,y) dx dy
	Triple integral sign	The triple integral of ...	integration	f(x,y,z) dx dy dz
	Line integral sign	The line integral of ...	integration	F dx
	Surface integral sign	The surface integral of ...	integration	F(x,y,z) dx dy
-	Subtraction sign Minus sign	... minus ... Negative...	Difference of two values, negative number	3 - 5 = -2
±	Plus/minus sign	... plus or minus ...	Expression of range, error, or tolerance	500 kbps ± 10%
	dot product sign	... dot ...	Scalar (dot) product of two vectors	A B = B A
x	Cross product sign	... cross ...	Vector (cross) product of two vectors	A x B = - (B x A)
	Product sign	The product of ...	Product of three up to infinitely many values
^	Carat	... to the power of ...	exponent	2 ^ 5 = 32
!	Exclamation	... factorial	Product of all positive integers up to a certain value	5! = 120
	surd	... root of ...	Algebraic expressions	z = (x + y)
	square root symbol	The square root of ...	Algebraic expressions
...	Continuation sign	... and so on up to ... ... and so on indefinitely	Extension of sequence	S = {1, 2, 3, ...}
/	Slash	... divided by ... ... over ...	Division	3/4 = 0.75
÷	Division sign	... divided by ...	Division	3 ÷ 4 = 0.75
	Percent symbol	... percent ...	Proportion	0.032 = 3.2
	Per mil symbol	... per mil ...	Proportion	0.032 = 32
:	Colon, ratio sign	... is to ... ... such that ... ... it is true that ...	Division or ratio, symbol following logical quantifier or used in defining a set	2:4 = 20:40 x : x > 4 and x < 5 x : x < 0 or x > -1 S = {x : x < 3}
|	Vertical line	... such that ... ...it is true that ...	Symbol following logical quantifier or used in defining a set	x | x > 4 and x < 5 x | x < 0 or x > -1 S = {x | x < 3}
::	Double colon	... averaged with ...	arithmetic mean	3 :: 11 = 7
	lemniscate	... infinity ... increases without limit	Infinite summations Infinite sequence Limit	x : x <
(  )	Parentheses	...quantity... ...list... ...set of coordinates... ...open interval	Denotes a quantity, list, set of coordinates, or an open interval	(x + y) + z (a1, a2, a3, a4) (x,y,z) (3,5)
[  ]	Square brackets	... the quantity ... ... the closed interval ...	Denotes a quantity or a closed interval	w + [(x + y) + z] [3,5]
(  ]	Hybrid brackets	... the half-open interval ...	Denotes a half-open interval	(3,5]
[  )	Hybrid brackets	... the half-open interval ...	Denotes a half-open interval	[3,5)
{  }	Curly brackets	... the quantity ... ... the set ...	Denotes a quantity or a set	E = {2, 4, 6, 8, ...}
=	Equal sign	... equals ...	Indicates two values are the same	-(-5) = 5 2z2 + 4z - 6 = 0
	proportionality sign	... is proportional to ...	Indicates two variables change in direct proportion	x  y
~	Similarity sign	... is similar to ...	Indicates two objects are geometrically similar	ABC ~ DEF
	Approximate equal sign	... is approximately equal to ...	Indicates two values are close to each other	x + y z
	Inequality sign	... is not equal to ...	Indicates two values are different	x y
<	Inequality sign	... is less than ...	Indicates value on left is smaller than value on right	3 < 5 x < y
	Inequality sign	... is less than or equal to ... ... is at most equal to ...	Indicates value on left is smaller than or equal to value on right	x y
>	Inequality sign	... is greater than ...	Indicates value on left is larger than value on right	5 > 3 x > y
	Inequality sign	... is greater than or equal to ...	Indicates value on left is larger than or equal to value on right	x y
|  |	absolute value sign	The absolute value of ...	Distance of value from origin in number line, plane, or space	| -3 | = 3
	increment sign, Triangle symbol	the change in ... triangle ...	Indicates a small change, Denotes vertices of triangle	m = y / x ABC = DEF
	Perpendicularity symbol	... is perpendicular to ...	Geometry	L M
//	Parallel symbol	... is parallel to ...	Geometry	L // M
	angle symbol	Angle ...	Geometry	ABC = DEF
	Existential quantifier	For some ... There exists a(n) ...	Logical statements	x : x > 4 and x < 5
	Universal quantifier	For all ... For every ...	Logical statements	x : x < 0 or x > -1
¬	Logical negation symbol	not ...	Logical statements	¬(¬A) A
	logical implication symbol	... implies ... If ... then ...	Logical statements	A B
	logical equivalence symbol	... is logically equivalent to ... ... if and only if ..	Logical statements	A B
	Three dots	... therefore ... ... it follows that ...	Logical statements or mathematical proofs	x = y and y = z x = z
	Element-of symbol	... is an element of a set ...	Sets	a A
	Not-element-of symbol	... is not an element of a set ...	Sets	b A
	Subset symbol	... is a subset of ...	Sets	A B
	Proper subset symbol	... is a proper subset of ...	Sets	A B
	Union symbol	... union ...	Sets	A B = B A
	Intersection symbol	... intersect ... ... intersected with ...	Sets	A B = B A
	Null symbol	The null set The empty set	Sets	= { }
	Hebrew aleph (uppercase)	Aleph ...	Transfinite cardinal	1 + 0 = 1
º	Degree symbol	... degree(s)	Angular measure Temperature	= 45º T = +20 ºC
	Greek theta (lowercase)	... theta ...	Angular variable	= 90º
	Greek phi (lowercase)	... phi ...	Angular variable	= 45º
	Greek lambda (lowercase)	... lambda ...	wavelength Ratio Eigenvalue Lebesgue measure	= 70 cm = 3:1
µ	Greek mu (lowercase)	micro- (10-6)	prefix multiplier	C = 0.001 µF
	Greek pi (lowercase)	... pi ...	General science	3.14159
	Greek omega (uppercase)	... omega ...	Volume of an object Ohms (resistance)	R2 = 330
	Greek omega (lowercase)	... omega ...	Transfinite ordinal Angular velocity Period	= 36,000 rad/s = 1/60 s
, N	Enhanced or bold N	The set of natural numbers	Number theory Set theory	= {0, 1, 2, 3, ...}
, Z	Enhanced or bold Z	The set of integers	Number theory Set theory	= {0, 1, -1, 2, -2, 3, -3, ...}
, Q	Enhanced or bold Q	The set of rational numbers	Number theory Set theory	= {a/b | a and b are in }
, R	Enhanced or bold R	The set of real numbers	Number theory Set theory	What is the cardinality of ?

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