Basic math symbols
| Symbol |
Symbol Name |
Meaning / definition |
Example |
| = |
equals sign |
equality |
5 = 2+35 is equal to 2+3 |
| ≠ |
not equal sign |
inequality |
5 ≠ 45 is not equal to 4 |
| ≈ |
approximately equal |
approximation |
sin(0.01) ≈ 0.01,x |
≈ y means x is approximately equal to y |
| > | strict inequality | greater than | 5 > 45 is greater than 4 | | < | strict inequality | less than | 4 < 54 is less than 5 | | ≥ | inequality | greater than or equal to | 5 ≥ 4,x ≥ y 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 | | + | plus sign | addition | 1 + 1 = 2 | | − | minus sign | 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 | | * | asterisk | multiplication | 2 * 3 = 6 | | × | times sign | multiplication | 2 × 3 = 6 | | · | multiplication dot | multiplication | 2 · 3 = 6 | | ÷ | division sign / obelus | division | 6 ÷ 2 = 3 | | / | division slash | division | 6 / 2 = 3 | | — | horizontal line | division / fraction | | | 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 | | 3√a | cube root | 3√a · 3√a · 3√a = a | 3√8 = 2 | | 4√a | fourth root | 4√a · 4√a · 4√a · 4√a = a | 4√16 = ±2 | | n√a | n-th root (radical) | | for n=3, n√8 = 2 | | % | percent | 1% = 1/100 | 10% × 30 = 3 | | ‰ | per-mille | 1‰ = 1/1000 = 0.1% | 10‰ × 30 = 0.3 | | ppm | per-million | 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° |
|
measured angle |
|
ABC = 30° |
|
spherical angle |
|
AOB = 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″ |
|
line |
infinite line |
|
| AB |
line segment |
line from point A to point B |
|
|
ray |
line that start from point A |
|
|
arc |
arc from point A to point B |
= 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 = π·d = 2·π·r | | 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 |
| ∞ |
lemniscate |
infinity symbol |
|
| ≪ |
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 |
factorial |
4! = 123*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 | a ≤ x ≤ b} | 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 | | | ∏ | 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 | Euler-Mascheroni constant | 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 = π·d = 2·π·r |
Linear Algebra Symbols
| Symbol |
Symbol Name |
Meaning / definition |
Example |
| · |
dot |
scalar product |
a · b |
| × |
cross |
vector product |
a × b |
| A⊗B |
tensor product |
tensor product of A and B |
A ⊗ B |
|
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(A ∩ B) |
probability of events intersection |
probability that of events A and B |
P(A∩B) = 0.5 |
| P(A ∪ B) |
probability of events union |
probability that of events A or B |
P(A∪B) = 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) | expectation value | 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 | variance of random variable X | var(X) = 4 | | σ2 | variance | variance of population values | σ2 = 4 | | std(X) | standard deviation | standard deviation of random variable X | std(X) = 2 | | σX | standard deviation | standard deviation value of random variable X | σX
= 2 | | | median | middle value of random variable x | | | 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 | | | ∑∑ | double summation | double summation | | | 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 X | distribution of random variable X | X ~ N(0,3) | | N(μ,σ2) | normal distribution | 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! |
factorial |
n! = 1·2·3·...·n |
5! = 1·2·3·4·5 = 120 |
| nPk |
permutation |
|
5P3 = |
5! / (5-3)! = 60 |
| nCk | combination | | 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 |
subset has fewer elements or equal to the set |
{9,14,28} ⊆ {9,14,28} |
| A ⊂ B |
proper subset / strict subset |
subset has fewer elements than the set |
{9,14} ⊂ {9,14,28} |
| A ⊄ B |
not subset |
left set not a subset of right set |
{9,66} ⊄ {9,14,28} |
| A ⊇ B |
superset |
set A has more elements or equal to the set B |
{9,14,28} ⊇ {9,14,28} |
| A ⊃ B |
proper superset / strict superset |
set A has more elements than set B |
{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 |
|
|
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} | | a∈A | element of | set membership | A={3,9,14}, 3 ∈ A | | x∉A | 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 | | | aleph-null | infinite cardinality of natural numbers set | | | | aleph-one | cardinality of countable ordinal numbers set | | | Ø | empty set | Ø = { } | C = {Ø} | | | universal set | set of all possible values | | | 0 | natural numbers / whole numbers set (with zero) | 0 = {0,1,2,3,4,...} | 0 ∈ 0 | | 1 | natural numbers / whole numbers set (without zero) | 1 = {1,2,3,4,5,...} | 6 ∈ 1 | | | integer numbers set | = {...-3,-2,-1,0,1,2,3,...} | -6 ∈ | | | rational numbers set | = {x | x=a/b, a,b∈} | 2/6 ∈ | | | real numbers set | = {x | -∞ < x <∞} | 6.343434∈ | | | complex numbers set | = {z | z=a+bi, -∞<a<∞, -∞<b<∞} | 6+2i ∈ |
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 |
|
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 |
derivative - Lagrange's notation |
(3x3)' = 9x2 |
| y '' |
second derivative |
derivative of derivative |
(3x3)'' = 18x |
| y(n) |
nth derivative |
n times derivation |
(3x3)(3) = 18 |
|
derivative |
derivative - Leibniz'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's notation |
|
|
time second derivative |
derivative of derivative |
|
| Dx y |
derivative |
derivative - Euler's notation |
|
| Dx2y |
second derivative |
derivative of derivative |
|
|
partial derivative |
|
∂(x2+y2)/∂x = 2x |
| ∫ |
integral |
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+bi → z*=a-bi |
z* = 3 - 2i |
| z |
complex conjugate |
z = a+bi → z = |
|
a-bi | z = 3 - 2i |
| ∇ | nabla / del | gradient / divergence operator | ∇f (x,y,z) | | | vector | | | | | unit vector | | | | x * y | convolution | y(t) = x(t) * h(t) | | | | Laplace transform | F(s) = {f (t)} | | | | Fourier transform | X(ω) = {f (t)} | | | δ | delta function | | | | ∞ | lemniscate | infinity symbol | |
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
| Greek Symbol |
Greek Letter Name |
English Equivalent |
Pronunciation |
|
| Upper Case |
Lower Case |
|
|
|
| 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 |
