Friday, 25 May 2018

Basic Maths symbols and Meanings


Basic math symbols
Symbol
Symbol Name
Meaning / definition
Example
=
equality
5 = 2+3
5 is equal to 2+3
not equal sign
inequality
5 ≠ 4
5 is not equal to 4
approximately equal
approximation
sin(0.01) ≈ 0.01,
xy means x is approximately equal to y
> 
strict inequality
greater than
5 > 4
5 is greater than 4
< 
strict inequality
less than
4 < 5
4 is less than 5
inequality
greater than or equal to
5 ≥ 4,
xy means x is greater than or equal to y
inequality
less than or equal to
4 ≤ 5,
x ≤ y means x is less than or equal to y
( )
parentheses
calculate expression inside first
2 × (3+5) = 16
[ ]
brackets
calculate expression inside first
[(1+2)×(1+5)] = 18
+
addition
1 + 1 = 2
subtraction
2 − 1 = 1
±
plus - minus
both plus and minus operations
3 ± 5 = 8 and -2
±
minus - plus
both minus and plus operations
3 5 = -2 and 8
*
multiplication
2 * 3 = 6
×
multiplication
2 × 3 = 6
multiplication
2 3 = 6
÷
division
6 ÷ 2 = 3
/
division
6 / 2 = 3
division / fraction
\frac{6}{2}=3
mod
modulo
remainder calculation
7 mod 2 = 1
.
period
decimal point, decimal separator
2.56 = 2+56/100
ab
power
exponent
23 = 8
a^b
caret
exponent
2 ^ 3 = 8
a
square root
a a  = a
√9 = ±3
3a
cube root
3a 3√a   3√a  = a
3√8 = 2
4a
fourth root
4a 4√a   4√a   4√a  = a
4√16 = ±2
na
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
ppb
per-billion
1ppb = 1/1000000000
10ppb × 30 = 3×10-7
ppt
per-trillion
1ppt = 10-12
10ppt × 30 = 3×10-10
Geometry symbols
Symbol
Symbol Name
Meaning / definition
Example
angle
formed by two rays
ABC = 30°
http://www.rapidtables.com/math/symbols/geometry_symbols/measured_angle.gif
measured angle

http://www.rapidtables.com/math/symbols/geometry_symbols/measured_angle.gifABC = 30°
http://www.rapidtables.com/math/symbols/geometry_symbols/spherical_angle.gif
spherical angle

http://www.rapidtables.com/math/symbols/geometry_symbols/spherical_angle.gifAOB = 30°
right angle
= 90°
α = 90°
°
degree
1 turn = 360°
α = 60°
deg
degree
1 turn = 360deg
α = 60deg
prime
arcminute, 1° = 60′
α = 60°59′
double prime
arcsecond, 1′ = 60″
α = 60°59′59″
http://www.rapidtables.com/math/symbols/geometry_symbols/line.gif
line
infinite line

AB
line segment
line from point A to point B

http://www.rapidtables.com/math/symbols/geometry_symbols/ray.gif
ray
line that start from point A

http://www.rapidtables.com/math/symbols/geometry_symbols/arc.gif
arc
arc from point A to point B
http://www.rapidtables.com/math/symbols/geometry_symbols/arc.gif= 60°
perpendicular
perpendicular lines (90° angle)
AC BC
| |
parallel
parallel lines
AB | | CD
congruent to
equivalence of geometric shapes and size
∆ABC ∆XYZ
~
similarity
same shapes, not same size
∆ABC~ ∆XYZ
Δ
triangle
triangle shape
ΔABC ΔBCD
|x-y|
distance
distance between points x and y
| x-y | = 5
π
pi constant
π = 3.141592654...
is the ratio between the circumference and diameter of a circle
c = πd = 2πr
rad
radians
radians angle unit
360° = 2π rad
c
radians
radians angle unit
360° = 2π c
grad
gradians / gons
grads angle unit
360° = 400 grad
g
gradians / gons
grads angle unit
360° = 400 g
Algebra symbols
Symbol
Symbol Name
Meaning / definition
Example
x
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
11 ~ 10
approximately equal
approximation
sin(0.01) ≈ 0.01
proportional to
proportional to
y x when y = kx, k constant

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
[ ]
brackets
calculate expression inside first
[(1+2)*(1+5)] = 18
{ }
braces
set

x
floor brackets
rounds number to lower integer
4.3 = 4
x
ceiling brackets
rounds number to upper integer
4.3 = 5
x!
exclamation mark
4! = 1*2*3*4 = 24
| x |
single vertical bar
absolute value
| -5 | = 5
f (x)
function of x
maps values of x to f(x)
f (x) = 3x+5
(f g)
function composition
(f g) (x) = f (g(x))
f (x)=3x,g(x)=x-1 (f g)(x)=3(x-1)
(a,b)
open interval
(a,b) = {x | a < x < b}
x (2,6)
[a,b]
closed interval
[a,b] = {x | axb}
x [2,6]
delta
change / difference
t = t1 - t0
discriminant
Δ = b2 - 4ac

sigma
summation - sum of all values in range of series
xi= x1+x2+...+xn
∑∑
sigma
double summation
http://www.rapidtables.com/math/symbols/statistical_symbols/double_sum_ex.gif
capital pi
product - product of all values in range of series
xi=x1∙x2∙...∙xn
e
e constant / Euler's number
e = 2.718281828...
e = lim (1+1/x)x , x→∞
γ
γ = 0.527721566...

φ
golden ratio
golden ratio constant

π
pi constant
π = 3.141592654...
is the ratio between the circumference and diameter of a circle
c = πd = 2πr
Linear Algebra Symbols
Symbol
Symbol Name
Meaning / definition
Example
·
dot
scalar product
a · b
×
cross
vector product
a × b
AB
tensor product
tensor product of A and B
A B
\langle x,y \rangle
inner product


[ ]
brackets
matrix of numbers

( )
parentheses
matrix of numbers

| A |
determinant
determinant of matrix A

det(A)
determinant
determinant of matrix A

|| x ||
double vertical bars
norm

AT
transpose
matrix transpose
(AT)ij = (A)ji
A
Hermitian matrix
matrix conjugate transpose
(A)ij = (A)ji
A*
Hermitian matrix
matrix conjugate transpose
(A*)ij = (A)ji
A -1
inverse matrix
A A-1 = I

rank(A)
matrix rank
rank of matrix A
rank(A) = 3
dim(U)
dimension
dimension of matrix A
rank(U) = 3
Probability and statistics symbols
Symbol
Symbol Name
Meaning / definition
Example
P(A)
probability function
probability of event A
P(A) = 0.5
P(AB)
probability of events intersection
probability that of events A and B
P(AB) = 0.5
P(A B)
probability of events union
probability that of events A or B
P(AB) = 0.5
P(A | B)
conditional probability function
probability of event A given event B occured
P(A | B) = 0.3
f (x)
probability density function (pdf)
P(a x b) = ∫ f (x) dx

F(x)
cumulative distribution function (cdf)
F(x) = P(X x)

μ
population mean
mean of population values
μ = 10
E(X)
expected value of random variable X
E(X) = 10
E(X | Y)
conditional expectation
expected value of random variable X given Y
E(X | Y=2) = 5
var(X)
variance of random variable X
var(X) = 4
σ2
variance of population values
σ2 = 4
std(X)
standard deviation of random variable X
std(X) = 2
σX
standard deviation value of random variable X
σX  = 2
http://www.rapidtables.com/math/symbols/statistical_symbols/median.GIF
median
middle value of random variable x
http://www.rapidtables.com/math/symbols/statistical_symbols/median_ex.GIF
cov(X,Y)
covariance
covariance of random variables X and Y
cov(X,Y) = 4
corr(X,Y)
correlation
correlation of random variables X and Y
corr(X,Y) = 0.6
ρX,Y
correlation
correlation of random variables X and Y
ρX,Y = 0.6
summation
summation - sum of all values in range of series
http://www.rapidtables.com/math/symbols/statistical_symbols/sum_ex.gif
∑∑
double summation
double summation
http://www.rapidtables.com/math/symbols/statistical_symbols/double_sum_ex.gif
Mo
mode
value that occurs most frequently in population

MR
mid-range
MR = (xmax+xmin)/2

Md
sample median
half the population is below this value

Q1
lower / first quartile
25% of population are below this value

Q2
median / second quartile
50% of population are below this value = median of samples

Q3
upper / third quartile
75% of population are below this value

x
sample mean
average / arithmetic mean
x = (2+5+9) / 3 = 5.333
s 2
sample variance
population samples variance estimator
s 2 = 4
s
sample standard deviation
population samples standard deviation estimator
s = 2
zx
standard score
zx = (x-x) / sx

X ~
distribution of random variable X
X ~ N(0,3)
N(μ,σ2)
gaussian distribution
X ~ N(0,3)
U(a,b)
uniform distribution
equal probability in range a,b 
X ~ U(0,3)
exp(λ)
exponential distribution
f (x) = λe-λx , x≥0

gamma(c, λ)
gamma distribution
f (x) = λ c xc-1e-λx / Γ(c), x≥0

χ 2(k)
chi-square distribution
f (x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) )

F (k1, k2)
F distribution


Bin(n,p)
binomial distribution
f (k) = nCk pk(1-p)n-k

Poisson(λ)
Poisson distribution
f (k) = λke-λ / k!

Geom(p)
geometric distribution
f (k) =  p(1-p) k

HG(N,K,n)
hyper-geometric distribution


Bern(p)
Bernoulli distribution


Combinatorics Symbols
Symbol
Symbol Name
Meaning / definition
Example
n!
n! = 123...n
5! = 12345 = 120
nPk
permutation
_{n}P_{k}=\frac{n!}{(n-k)!}
5P3 = 5! / (5-3)! = 60
nCk

http://www.rapidtables.com/math/symbols/math_symbols/combination.GIF
combination
_{n}C_{k}=\binom{n}{k}=\frac{n!}{k!(n-k)!}
5C3 = 5!/[3!(5-3)!]=10
Set theory symbols
Symbol
Symbol Name
Meaning / definition
Example
{ }
set
a collection of elements
A = {3,7,9,14},
B = {9,14,28}
A ∩ B
intersection
objects that belong to set A and set B
A ∩ B = {9,14}
A B
union
objects that belong to set A or set B
A B = {3,7,9,14,28}
A B
subset
A is a subset of B. set A is included in set B.
{9,14,28} {9,14,28}
A B
proper subset / strict subset
A is a subset of B, but A is not equal to B.
{9,14} {9,14,28}
A B
not subset
set A is not a subset of set B
{9,66} {9,14,28}
A B
superset
A is a superset of B. set A includes set B
{9,14,28} {9,14,28}
A B
proper superset / strict superset
A is a superset of B, but B is not equal to A.
{9,14,28} {9,14}
A B
not superset
set A is not a superset of set B
{9,14,28} {9,66}
2A
power set
all subsets of A

\mathcal{P}(A)
power set
all subsets of A

A = B
equality
both sets have the same members
A={3,9,14},
B={3,9,14},
A=B
Ac
complement
all the objects that do not belong to set A

A \ B
relative complement
objects that belong to A and not to B
A = {3,9,14},
B = {1,2,3},
A-B = {9,14}
A - B
relative complement
objects that belong to A and not to B
A = {3,9,14},
B = {1,2,3},
A-B = {9,14}
A ∆ B
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}
A B
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}
aA
element of
set membership
 A={3,9,14}, 3 A
xA
not element of
no set membership
A={3,9,14}, 1 A
(a,b)
ordered pair
collection of 2 elements

A×B
cartesian product
set of all ordered pairs from A and B

|A|
cardinality
the number of elements of set A
A={3,9,14}, |A|=3
#A
cardinality
the number of elements of set A
A={3,9,14}, #A=3
http://www.rapidtables.com/math/symbols/set_symbols/aleph-null.gif
aleph-null
infinite cardinality of natural numbers set

http://www.rapidtables.com/math/symbols/set_symbols/aleph-one.gif
aleph-one
cardinality of countable ordinal numbers set

Ø
empty set
Ø = { }
C = {Ø}
\mathbb{U}
universal set
set of all possible values

\mathbb{N}0
natural numbers / whole numbers  set (with zero)
\mathbb{N}0 = {0,1,2,3,4,...}
0 \mathbb{N}0
\mathbb{N}1
natural numbers / whole numbers  set (without zero)
\mathbb{N}1 = {1,2,3,4,5,...}
6 \mathbb{N}1
\mathbb{Z}
integer numbers set
\mathbb{Z}= {...-3,-2,-1,0,1,2,3,...}
-6 \mathbb{Z}
\mathbb{Q}
rational numbers set
\mathbb{Q}= {x | x=a/b, a,b\mathbb{Z}}
2/6 \mathbb{Q}
\mathbb{R}
real numbers set
\mathbb{R}= {x | -∞ < x <∞}
6.343434\mathbb{R}
\mathbb{C}
complex numbers set
\mathbb{C}= {z | z=a+bi, -∞<a<∞,      -∞<b<∞}
6+2i \mathbb{C}
Logic symbols
Symbol
Symbol Name
Meaning / definition
Example
and
and
x y
^
caret / circumflex
and
x ^ y
&
ampersand
and
x & y
+
plus
or
x + y
reversed caret
or
x y
|
vertical line
or
x | y
x'
single quote
not - negation
x'
x
bar
not - negation
x
¬
not
not - negation
¬ x
!
exclamation mark
not - negation
! x
circled plus / oplus
exclusive or - xor
x y
~
tilde
negation
~ x
implies


equivalent
if and only if (iff)

equivalent
if and only if (iff)

for all


there exists


there does not exists


therefore


because / since


Calculus & analysis symbols
Symbol
Symbol Name
Meaning / definition
Example
\lim_{x\to x0}f(x)
limit
limit value of a function

ε
epsilon
represents a very small number, near zero
ε 0
e
e constant / Euler's number
e = 2.718281828...
e = lim (1+1/x)x , x→∞
y '
derivative - Lagrange's notation
(3x3)' = 9x2
y ''
second derivative
derivative of derivative
(3x3)'' = 18x
y(n)
nth derivative
n times derivation
(3x3)(3) = 18
\frac{dy}{dx}
derivative - Leibniz's notation
d(3x3)/dx = 9x2
\frac{d^2y}{dx^2}
second derivative
derivative of derivative
d2(3x3)/dx2 = 18x
\frac{d^ny}{dx^n}
nth derivative
n times derivation

\dot{y}
time derivative
derivative by time - Newton's notation

http://www.rapidtables.com/math/symbols/math_symbols/time_drivative_II.GIF
time second derivative
derivative of derivative

Dx y
derivative - Euler's notation

Dx2y
second derivative
derivative of derivative

\frac{\partial f(x,y)}{\partial x}
partial derivative

∂(x2+y2)/∂x = 2x
opposite to derivation
f(x)dx
∫∫
double integral
integration of function of 2 variables
∫∫ f(x,y)dxdy
∫∫∫
triple integral
integration of function of 3 variables
∫∫∫ f(x,y,z)dxdydz
closed contour / line integral


closed surface integral


closed volume integral


[a,b]
closed interval
[a,b] = {x | a x b}

(a,b)
open interval
(a,b) = {x | a < x < b}

i
imaginary unit
i ≡ √-1
z = 3 + 2i
z*
complex conjugate
z = a+biz*=a-bi
z* = 3 - 2i
z
complex conjugate
z = a+biz = a-bi
z = 3 - 2i
nabla / del
gradient / divergence operator
f (x,y,z)
http://www.rapidtables.com/math/symbols/math_symbols/vector.GIF
vector


http://www.rapidtables.com/math/symbols/math_symbols/unit%20vector.GIF
unit vector


x * y
y(t) = x(t) * h(t)

http://www.rapidtables.com/math/symbols/calculus_symbols/L.gif
F(s) = http://www.rapidtables.com/math/symbols/calculus_symbols/L.gif{f (t)}

http://www.rapidtables.com/math/symbols/calculus_symbols/F.gif
Fourier transform
X(ω) = http://www.rapidtables.com/math/symbols/calculus_symbols/F.gif{f (t)}

δ
delta function



Numeral symbols
Name
European
Roman
Hindu Arabic
Hebrew
zero
0

٠

one
1
I
١
א
two
2
II
٢
ב
three
3
III
٣
ג
four
4
IV
٤
ד
five
5
V
٥
ה
six
6
VI
٦
ו
seven
7
VII
٧
ז
eight
8
VIII
٨
ח
nine
9
IX
٩
ט
ten
10
X
١٠
י
eleven
11
XI
١١
יא
twelve
12
XII
١٢
יב
thirteen
13
XIII
١٣
יג
fourteen
14
XIV
١٤
יד
fifteen
15
XV
١٥
טו
sixteen
16
XVI
١٦
טז
seventeen
17
XVII
١٧
יז
eighteen
18
XVIII
١٨
יח
nineteen
19
XIX
١٩
יט
twenty
20
XX
٢٠
כ
thirty
30
XXX
٣٠
ל
forty
40
XL
٤٠
מ
fifty
50
L
٥٠
נ
sixty
60
LX
٦٠
ס
seventy
70
LXX
٧٠
ע
eighty
80
LXXX
٨٠
פ
ninety
90
XC
٩٠
צ
one hundred
100
C
١٠٠
ק

Greek alphabet letters
Upper Case Letter
Lower Case Letter
Greek Letter Name
English Equivalent
Letter Name Pronounce
Α
α
Alpha
a
al-fa
Β
β
Beta
b
be-ta
Γ
γ
Gamma
g
ga-ma
Δ
δ
Delta
d
del-ta
Ε
ε
Epsilon
e
ep-si-lon
Ζ
ζ
Zeta
z
ze-ta
Η
η
Eta
h
eh-ta
Θ
θ
Theta
th
te-ta
Ι
ι
Iota
i
io-ta
Κ
κ
Kappa
k
ka-pa
Λ
λ
Lambda
l
lam-da
Μ
μ
Mu
m
m-yoo
Ν
ν
Nu
n
noo
Ξ
ξ
Xi
x
x-ee
Ο
ο
Omicron
o
o-mee-c-ron
Π
π
Pi
p
pa-yee
Ρ
ρ
Rho
r
row
Σ
σ
Sigma
s
sig-ma
Τ
τ
Tau
t
ta-oo
Υ
υ
Upsilon
u
oo-psi-lon
Φ
φ
Phi
ph
f-ee
Χ
χ
Chi
ch
kh-ee
Ψ
ψ
Psi
ps
p-see
Ω
ω
Omega
o
o-me-ga
Roman numerals
Number
Roman numeral
0
not defined
1
I
2
II
3
III
4
IV
5
V
6
VI
7
VII
8
VIII
9
IX
10
X
11
XI
12
XII
13
XIII
14
XIV
15
XV
16
XVI
17
XVII
18
XVIII
19
XIX
20
XX
30
XXX
40
XL
50
L
60
LX
70
LXX
80
LXXX
90
XC
100
C
200
CC
300
CCC
400
CD
500
D
600
DC
700
DCC
800
DCCC
900
CM
1000
M
5000
V
10000
X
50000
L
100000
C
500000
D
1000000
M