数学符号表
Mathematical Symbols
List of all mathematical symbols and signs - meaning and examples.
Basic math symbols
Symbol Name
Meaning / definition
not equal sign
inequality
strict inequality
greater than
strict inequality
inequality
greater than or equal to
inequality
less than or equal to
parentheses
calculate expression inside first
calculate expression inside first
subtraction
plus - minus
both plus and minus operations
minus - plus
both minus and plus operations
multiplication
multiplication
multiplication
division / fraction
remainder calculation
decimal point, decimal separator
square root
fourth root
4√&·&4&·&4&·&4&=
n-th root (radical)
per-billion
per-trillion
Geometry symbols
Symbol Name
Meaning / definition
formed by two rays
measured angle
spherical angle
right angle
infinite line
line segment
line from point A to point B
line that start from point A
arc from point A to point B
perpendicular
perpendicular lines (90&angle)
parallel lines
congruent to
equivalence of geometric shapes and size
similarity
same shapes, not same size
triangle shape
distance between points x and y
pi constant
radians angle unit
grads angle unit
Algebra symbols
Symbol Name
Meaning / definition
x variable
unknown value to find
equivalence
identical to
equal by definition
equal by definition
equal by definition
equal by definition
approximately equal
weak approximation
approximately equal
approximation
proportional to
proportional to
much less than
much less than
much greater than
much greater than
parentheses
calculate expression inside first
calculate expression inside first
floor brackets
rounds number to lower integer
ceiling brackets
rounds number to upper integer
exclamation mark
single vertical bar
absolute value
function of x
maps values of x to f(x)
function composition
open interval
closed interval
change / difference
discriminant
summation - sum of all values in range of series
double summation
capital pi
product - product of all values in range of series
&/ Euler's number
golden ratio
golden ratio constant
pi constant
Linear Algebra Symbols
Symbol Name
Meaning / definition
scalar product
vector product
tensor product
tensor product of A and B
inner product
matrix of numbers
parentheses
matrix of numbers
determinant
determinant of matrix A
determinant
determinant of matrix A
double vertical bars
matrix transpose
Hermitian matrix
matrix conjugate transpose
Hermitian matrix
matrix conjugate transpose
inverse matrix
matrix rank
rank of matrix A
dimension of matrix A
Probability and statistics symbols
Symbol Name
Meaning / definition
probability function
probability of event A
probability of events intersection
probability that of events A and B
probability of events union
probability that of events A or B
conditional probability function
probability of event A given event B occured
probability density function (pdf)
cumulative distribution function (cdf)
population mean
mean of population values
expected value of random variable X
conditional expectation
expected value of random variable X given Y
variance of random variable X
variance of population values
standard deviation of random variable X
standard deviation value of random variable X
middle value of random variable x
covariance
covariance of random variables X and Y
correlation
correlation of random variables X and Y
correlation
correlation of random variables X and Y
summation - sum of all values in range of series
double summation
double summation
value that occurs most frequently in population
sample median
half the population is below this value
lower / first quartile
25% of population are below this value
median / second quartile
50% of population are below this value = median of samples
upper / third quartile
75% of population are below this value
sample mean
average / arithmetic mean
sample variance
population samples variance estimator
sample standard deviation
population samples standard deviation estimator
standard score
distribution of random variable X
gaussian distribution
uniform distribution
equal probability in range a,b&
exponential distribution
gamma distribution
chi-square distribution
F distribution
binomial distribution
Poisson distribution
geometric distribution
hyper-geometric distribution
Bernoulli distribution
Combinatorics Symbols
Symbol Name
Meaning / definition
permutation
combination
Set theory symbols
Symbol Name
Meaning / definition
a collection of elements
intersection
objects that belong to set A and set B
objects that belong to set A or set B
subset has fewer elements or equal to the set
proper subset / strict subset
subset has fewer elements than the set
not subset
left set not a subset of right set
set A has more elements or equal to the set B
proper superset / strict superset
set A has more elements than set B
not superset
set A is not a superset of set B
all subsets of A
all subsets of A
both sets have the same members
complement
all the objects that do not belong to set A
relative complement
objects that belong to A and not to B
relative complement
objects that belong to A and not to B
symmetric difference
objects that belong to A or B but not to their intersection
symmetric difference
objects that belong to A or B but not to their intersection
element of
set membership
not element of
no set membership
ordered pair
collection of 2 elements
cartesian product
set of all ordered pairs from A and B
cardinality
the number of elements of set A
cardinality
the number of elements of set A
aleph-null
infinite cardinality of natural numbers set
cardinality of countable ordinal numbers set
universal set
set of all possible values
natural numbers / whole numbers& set (with zero)
natural numbers / whole numbers& set (without zero)
integer numbers set
rational numbers set
real numbers set
complex numbers set
Logic symbols
Symbol Name
Meaning / definition
caret / circumflex
reversed caret
vertical line
single quote
not - negation
not - negation
not - negation
exclamation mark
not - negation
circled plus / oplus
exclusive or - xor
equivalent
if and only if (iff)
equivalent
if and only if (iff)
there exists
there does not exists
because / since
Calculus & analysis symbols
Symbol Name
Meaning / definition
limit value of a function
represents a very small number, near zero
&/ Euler's number
derivative - Lagrange's notation
second derivative
derivative of derivative
nth derivative
n times derivation
derivative - Leibniz's notation
second derivative
derivative of derivative
nth derivative
n times derivation
time derivative
derivative by time - Newton's notation
time second derivative
derivative of derivative
derivative - Euler's notation
second derivative
derivative of derivative
partial derivative
opposite to derivation
double integral
integration of function of 2 variables
triple integral
integration of function of 3 variables
closed contour / line integral
closed surface integral
closed volume integral
closed interval
open interval
imaginary unit
complex conjugate
complex conjugate
nabla / del
gradient / divergence operator
unit vector
Fourier transform
delta function
Numeral symbols
Hindu Arabic
one hundred
Greek alphabet letters
Greek Symbol
Greek Letter Name
English Equivalent
Pronunciation
Upper Case
Lower Case
o-mee-c-ron
oo-psi-lon
Roman numerals
Roman numeral
看过本文的人也看了：
我要留言技术领域：
取消收藏确定要取消收藏吗？
删除图谱提示你保存在该图谱下的知识内容也会被删除，建议你先将内容移到其他图谱中。你确定要删除知识图谱及其内容吗？
删除节点提示无法删除该知识节点，因该节点下仍保存有相关知识内容！
删除节点提示你确定要删除该知识节点吗？数学中因为用什么符号表示
数学中因为用什么符号表示
09-09-15 &匿名提问
见下面3个点
请登录后再发表评论!
　　这5个数，可以统一在一个公式中：e^(iπ)+1=0　　1、数字0　　0是极为重要的数字，0的发现被称为人类伟大的发现之一。0在我国古代叫做金元数字，意即极为珍贵的数字。0这个数据说是由印度人在约公元5世纪时发明，在1202年时，一个商人写了一本算盘之书，在东方中由于数学是以运算为主(西方当时以几何和逻辑为主)，由于运算上的需要，自然地引入了0这个数。在中国很早便有0这个数字很多文献都有记载。　　在1208年时将印度的阿拉伯数字引入本书，并在开头写了“印度人的9个数字，加上阿拉伯人发明的0符号便可以写出所有数字……”由于一些原因，在初时引入0这个符号到西方时，曾经引起西方人的困惑，因当时西方认为所有数都是可数，而且0这个数字会使很多算式，逻辑不能成立(如除0)，甚至认为是魔鬼数字，而被禁用。直至约公元15、16世纪，0和负数才逐渐给西方人所认同，才使西方数学有快速发展。　　0的另一个历史：0的发现始于印度。公元前2500年左右，印度最古老的文献《吠陀》已有“0”这个符号的应用，当时的0在印度表示空的位置。约在6世纪初，印度开始使用命位记数法。7世纪初印度大数学家葛拉夫•玛格蒲达首先说明了0的性质：任何数乘0是0，任何数加上0或减去0得任何数。遗憾的是，他并没有提到以命位记数法来进行计算的实例。也有的学者认为，0的概念之所以在印度产生并得以发展，是因为印度佛教中存在着“绝对无”这一哲学思想。公元733年，印度一位天文学家在访问现伊拉克首都巴格达期间，将印度的这种记数法介绍给了阿拉伯人，因为这种方法简便易行，不久就取代了在此之前的阿拉伯数字。这套记数法后来又传入西欧。　　2、圆周率π　　很早以前，人们就看出，圆的周长和直经的比，是个与圆的大小无关的常数，并称之为圆周率。1600年，英国威廉•奥托兰特首先使用π表示圆周率。1737年欧拉在其著作中使用π，后来被数学家广泛接受，一直没用至今。　　π是一个非常重要的常数。一位德国数学家评论道：“历史上一个国家所算得的圆周率的准确程度，可以做为衡量这个这国家当时数学发展水平的重要标志。”　　3、自然数e　　在微积分发明之前半个世纪，就有人提到这个数，所以虽然它在微积分里常常出现，却不是随著微积分诞生的。那么是在怎样的状况下导致它出现的呢？一个很可能的解释是，这个数和计算利息有关。　　我们都知道复利计息是怎么回事，就是利息也可以并进本金再生利息。但是本利和的多寡，要看计息周期而定，以一年来说，可以一年只计息一次，也可以每半年计息一次，或者一季一次，一月一次，甚至一天一次；当然计息周期愈短，本利和就会愈高。有人因此而好奇，如果计息周期无限制地缩短，比如说每分钟计息一次，甚至每秒，或者每一瞬间(理论上来说)，会发生什么状况？本利和会无限制地加大吗？答案是不会，它的值会稳定下来，趋近於一极限值，而e这个数就现身在该极限值当中(当然那时候还没给这个数取名字叫e)。所以用现在的数学语言来说，e可以定义成一个极限值，但是在那时候，根本还没有极限的观念，因此e的值应该是观察出来的，而不是用严谨的证明得到的。　　4、虚数i　　1484年，法国数学家舒克在他的著作《算术三论》中，解二次方程x^2-3x+4=0时，出现了虚数——两个共轭虚数。他声称，这是不可能的。　　在很长时间里，人们把虚数看作不可接受的“虚数”，谁也说不出它们有什么用处。随着时间的推移，人们才逐步认识了虚数的本质。　　1703年，法国数学家棣莫佛发现了公式：(cosθ+isinθ)^ｎ＝cosnθ+isinnθ，后来被人们称作棣莫佛定理。　　1732年，欧拉成功地给出了卡尔达诺曾经研究过的三次方程x^3+ｐx+ｑ=0(ｐ＞0，ｑ＞0)的三个根的一般公式。于1748年发现了著名的欧拉公式：e^(iθ)=cosθ+isin。1777年，欧拉在递交给彼得堡科学院的论文《微分方程》中，首次使用符号i表示(-1)的一个平方根，并系统地建立了复数的理论。　　1747年，法国数学家达朗贝尔发现，对于虚数按多项式的四则运算进行，则它们的结果都可以写成a+bi(其中a、b是实数)的形式。　　1797年，挪威测量学家威塞尔在递交给丹麦科学院的论文中，给出了复数的几何意义，正式提出把复数a+bi用平面上的点(a,b)来表示，用平面上的向量表示，初步建立了复平面的概念，真正作出了虚数的几何解释。　　1806年，德国数学家高斯发现并公布了虚数的图象法，1831年给出了复数的几何表示的详细说明。他采用有序数对(a,b)代表复数a+bi，把复数的和与积用纯代数法定义，给复数代数化，第一次深刻地揭露了复数的“数”的性质，也是高斯在1832年首先使用并提出了“复数”这个名词。　　1906年，日内瓦的阿工第一次用“模”这个词表示向量a+bi的长度。　　从1484年到1832年，在几百年内，经过许多数学家的长期努力，终于揭开了“虚数”的神秘面纱，显出它们的庐山真面目——“虚数不虚”。
数学中最重要的五个数（0、1、π、e、i）分别是谁在什么时候发现的？用0,1,π,e,i可以组成公式：e^(iπ)+1=0
请登录后再发表评论!
请登录后再发表评论!
请登录后再发表评论!
二楼的看清题目再答！！！！！
请登录后再发表评论!
像“众”字的两个点
请登录后再发表评论!Mathematical Symbols
List of all mathematical symbols and signs - meaning and examples.
Basic math symbols
SymbolSymbol NameMeaning / definitionExample
not equal sign
inequality
strict inequality
greater than
strict inequality
inequality
greater than or equal to
inequality
less than or equal to
parentheses
calculate expression inside first
2 & (3+5) = 16
calculate expression inside first
[(1+2)*(1+5)] = 18
subtraction
plus - minus
both plus and minus operations
3 & 5 = 8 and -2
minus - plus
both minus and plus operations
multiplication
multiplication
multiplication
division / fraction
remainder calculation
7 mod 2 = 1
decimal point, decimal separator
2.56 = 2+56/100
square root
&a&&&&a&&= a
forth root
n-th root (radical)
for&n=3,&n&8&= 2
1% = 1/100
10% & 30 = 3
1& = 1/1000 = 0.1%
10& & 30 = 0.3
1ppm = 1/1000000
10ppm & 30 = 0.0003
per-billion
10ppb & 30 = 3&10-7
per-trillion
1ppb = 10-12
10ppb & 30 = 3&10-10
Geometry symbols
SymbolSymbol NameMeaning / definitionExample
formed by two rays
measured angle
spherical angle
right angle
1 turn = 360&
line from point A to point B
line that start from point A
perpendicular
perpendicular lines (90angle)
parallel lines
congruent to
equivalence of geometric shapes and size
?ABC&&&?XYZ
similarity
same shapes, not same size
?ABC&~&?XYZ
triangle shape
&DABC&&&&DBCD
distance between points x and y
|&x-y&| = 5
pi constant
is the ratio between the circumference and diameter of a circle
c&=&&&d&= 2&&&r
radians angle unit
360&= 2& rad
grads angle unit
360&= 400 grad
Algebra symbols
SymbolSymbol NameMeaning / definitionExample
x variable
unknown value to find
when 2x&= 4, then&x&= 2
equivalence
identical to
equal by definition
equal by definition
equal by definition
equal by definition
approximately equal
weak approximation
approximately equal
approximation
sin(0.01) & 0.01
proportional to
proportional to
f(x)&&&g(x)
much less than
much less than
1&<<&1000000
much greater than
much greater than
1000000&>>&1
parentheses
calculate expression inside first
2 * (3+5) = 16
calculate expression inside first
[(1+2)*(1+5)] = 18
floor brackets
rounds number to lower integer
ceiling brackets
rounds number to upper integer
exclamation mark
4! = 1*2*3*4 = 24
single vertical bar
absolute value
| -5 | = 5
function of x
maps values of x to f(x)
f&(x) = 3x+5
function composition
(f&?g)&(x) =&f&(g(x))
f&(x)=3x,&g(x)=x-1&&rA(f&?g)(x)=3(x-1)&
open interval
(a,b)&?&{x&|&a&&&x&&&b}
closed interval
[a,b]&?&{x&|&a&&&x&&&b}
change / difference
?t&=&t1&-&t0
discriminant
&D =&b2&- 4ac
summation - sum of all values in range of series
&&xi= x1+x2+...+xn
double summation
capital pi
product - product of all values in range of series
&&xi=x1?x2?...?xn
&/ Euler's number
e&= lim (1+1/x)x&,&x&&
golden ratio
golden ratio constant
Linear Algebra Symbols
SymbolSymbol NameMeaning / definitionExample
scalar product
vector product
tensor product
tensor product of A and B
inner product
matrix of numbers
parentheses
matrix of numbers
determinant
determinant of matrix A
determinant
determinant of matrix A
double vertical bars
matrix transpose
(AT)ij&= (A)ji
Hermitian matrix
matrix conjugate transpose
(A&)ij&= (A)ji
Hermitian matrix
matrix conjugate transpose
(A*)ij&= (A)ji
inverse matrix
matrix rank
rank of matrix A
rank(A) = 3
dimension of matrix A
rank(U) = 3
Probability and statistics symbols
SymbolSymbol NameMeaning / definitionExample
probability function
probability of event A
P(A) = 0.5
probability of events intersection
probability that of events A and B
P(A&B) = 0.5
probability of events union
probability that of events A or B
P(A&B) = 0.5
conditional probability function
probability of event A given event B occured
P(A | B) = 0.3
probability density function (pdf)
P(a&&&x&&&b) =&& f&(x)&dx
cumulative distribution function (cdf)
F(x) =&P(X&&&x)
population mean
mean of population values
expected value of random variable X
conditional expectation
expected value of random variable X given Y
E(X | Y=2) = 5
variance of random variable X
var(X) = 4
variance of population values
standard deviation of random variable X
std(X) = 2
standard deviation value of random variable X
middle value of random variable x
covariance
covariance of random variables X and Y
cov(X,Y) = 4
correlation
correlation of random variables X and Y
corr(X,Y) = 3
correlation
correlation of random variables X and Y
summation - sum of all values in range of series
double summation
double summation
value that occurs most frequently in population
MR&= (xmax+xmin)/2
sample median
half the population is below this value
lower / first quartile
25% of population are below this value
median / second quartile
50% of population are below this value = median of samples
upper / third quartile
75% of population are below this value
sample mean
average / arithmetic mean
x&= (2+5+9) / 3 = 5.333
sample variance
population samples variance estimator
sample standard deviation
population samples standard deviation estimator
standard score
zx&= (x-x) /&sx
distribution of random variable X
X&~&N(0,3)
gaussian distribution
X&~&N(0,3)
uniform distribution
equal probability in range a,b&
X&~&U(0,3)
exponential distribution
f&(x)&= &e-&x&,&x&0
gamma(c, &)
gamma distribution
f&(x)&= & c xc-1e-&x&/ &G(c),x&0
chi-square distribution
f&(x)&= xk/2-1e-x/2&/ ( 2k/2&G(k/2) )
F&(k1, k2)
F distribution
binomial distribution
f&(k)&=&nCk&pk(1-p)n-k
Poisson(&)
Poisson distribution
f&(k)&= &ke-&&/&k!
geometric distribution
f&(k)&=& p&(1-p)&k
hyper-geometric distribution
Bernoulli distribution
Combinatorics Symbols
SymbolSymbol NameMeaning / definitionExample
n! = 1&2&3&...&n
5! = 1&2&3&4&5 = 120
permutation
5P3&=&5! / (5-3)! = 60
combination
5C3&=&5!/[3!(5-3)!]=10
Set theory symbols
SymbolSymbol NameMeaning / definitionExample
a collection of elements
A={3,7,9,14}, B={9,14,28}
intersection
objects that belong to set A and set B
A&&&B = {9,14}
objects that belong to set A or set B
A&&&B = {3,7,9,14,28}
subset has less elements or equal to the set
{9,14,28}&&&{9,14,28}
proper subset / strict subset
subset has less elements than the set
{9,14}&&&{9,14,28}
not subset
left set not a subset of right set
{9,66}&&&{9,14,28}
set A has more elements or equal to the set B
{9,14,28}&&&{9,14,28}
proper superset / strict superset
set A has more elements than set B
{9,14,28}&&&{9,14}
not superset
set A is not a superset of set B
{9,14,28}&?&{9,66}
all subsets of A
all subsets of A
both sets have the same members
A={3,9,14}, B={3,9,14}, A=B
complement
all the objects that do not belong to set A
relative complement
objects that belong to A and not to B
A={3,9,14},&&&& B={1,2,3}, A-B={9,14}
relative complement
objects that belong to A and not to B
A={3,9,14},&&&& B={1,2,3}, A-B={9,14}
symmetric difference
objects that belong to A or B but not to their intersection
A={3,9,14},&&&& B={1,2,3}, A ? B={1,2,9,14}
symmetric difference
objects that belong to A or B but not to their intersection
A={3,9,14},&&&& B={1,2,3}, A&?B={1,2,9,14}
element of
set membership
A={3,9,14}, 3&&&A
not element of
no set membership
A={3,9,14}, 1&&&A
ordered pair
collection of 2 elements
cartesian product
set of all ordered pairs from A and B
cardinality
the number of elements of set A
A={3,9,14}, |A|=3
cardinality
the number of elements of set A
A={3,9,14}, #A=3
infinite cardinality
universal set
set of all possible values
natural numbers set (with zero)
N0&= {0,1,2,3,4,...}
natural numbers set (without zero)
N1&= {1,2,3,4,5,...}
integer numbers set
Z&= {...-3,-2,-1,0,1,2,3,...}
rational numbers set
Q&= {x&|&x=a/b,&a,b&N}
real numbers set
R&= {x&| -& &&x&&&}
6.343434&& R
complex numbers set
C&= {z&|&z=a+bi, -&&a&&,&&&&& -&&b&&}
Logic symbols
SymbolSymbol NameMeaning / definitionExample
caret / circumflex
reversed caret
vertical line
single quote
not - negation
not - negation
not - negation
exclamation mark
not - negation
circled plus / oplus
exclusive or - xor
equivalent
if and only if
there exists
there does not exists
because / since
Calculus & analysis symbols
SymbolSymbol NameMeaning / definitionExample
limit value of a function
represents a very small number, near zero
&/ Euler's number
e&= lim (1+1/x)x&,&x&&
derivative - Leibniz's notation
(3x3)' = 9x2
second derivative
derivative of derivative
(3x3)'' = 18x
nth derivative
n times derivation
(3x3)(3)&= 18
derivative - Lagrange's notation
d(3x3)/dx&= 9x2
second derivative
derivative of derivative
d2(3x3)/dx2&= 18x
nth derivative
n times derivation
time derivative
derivative by time - Newton notation
time second derivative
derivative of derivative
partial derivative
&(x2+y2)/&x&= 2x
opposite to derivation
double integral
integration of function of 2 variables
triple integral
integration of function of 3 variables
closed contour / line integral
closed surface integral
closed volume integral
closed interval
[a,b] = {x&|&a&&&x&&&b}
open interval
(a,b) = {x&|&a&&&x&&&b}
imaginary unit
z&= 3 + 2i
complex conjugate
z&=&a+bi&&&z*=a-bi
z*&= 3 + 2i
complex conjugate
z&=&a+bi&&&z&=&a-bi
z&= 3 + 2i
nabla / del
gradient / divergence operator
&f&(x,y,z)
unit vector
y(t) =&x(t) *&h(t)
F(s) =&L{f&(t)}
Fourier transform
X(&) =&F{f&(t)}
delta function
Numeral symbols
NameEuropeanRomanHindu ArabicHebrew
one hundred
Greek alphabet letters
Greek SymbolGreek Letter NameEnglish EquivalentPronunciation
Upper CaseLower Case
o-mee-c-ron
oo-psi-lon
Roman numerals
NumberRoman numeral
阅读(...) 评论()}