Download Mathematical Notation Numbers Notation Meaning Example N

Mathematical Notation
Numbers
Notation
N
Meaning
Natural numbers
Z
R
|x|
a
a/b or
b
a|b m
m
Cn or
n
n!
b
X
xi
Integers
Real numbers
modulus
a over b
Example
1, 2, 3, . . .
(some people include 0)
. . .√
, −2, −1, 0, 1, 2, . . .
1
, 2, π, . . .
2
|2| = 2, |−3| = 3
12/3 = 4, 2/4 = 0.5
a divides b
4 | 12
m choose n
5
n factorial
5! = 120
3
X
i2 = 12 + 22 + 32 = 14
xa + xa+1 + · · · + xb
i=a
C2 = 10
i=1
Sets
Notation
{. . .}
Meaning
a set
x∈A
{x : . . .} or {x | . . .}
|A|
x is an element of the set A
the set of all x such that . . .
cardinality of A
(number of elements in A)
A union B
(set of elements in either A or B)
A intersection B
(set of elements in both A and B)
set difference
(set of elements in A but not B)
A is a subset of B (or equal)
complement of A
empty set (no elements)
ordered pair
Cartesian product
(set of all ordered pairs)
A∪B
A∩B
A\B
A⊆B
A0
∅
(x, y)
A×B
1
Example
{1, 2, 3}
NOTE: {1, 2} = {2, 1}
2 ∈ {1, 2, 3}
{x : x2 = 4} = {−2, 2}
|{1, 2, 3}| = 3
{1, 2, 3} ∪ {2, 4} = {1, 2, 3, 4}
{1, 2, 3} ∩ {2, 4} = {2}
{1, 2, 3} \ {2, 4} = {1, 3}
{1, 3} ⊆ {1, 2, 3}
everything not in A
{1, 2} ∩ {3, 4} = ∅
NOTE: (1, 2) 6= (2, 1)
{1, 2} × {1, 3} =
{(1, 1), (2, 1), (1, 3), (2, 3)}
The Greek alphabet
You don’t need to learn this;
keep it for reference. Apologies to Greek students: you
may not recognise this, but
it is the Greek alphabet that
mathematicians use!
Name
Capital
alpha
A
beta
B
gamma
Γ
delta
∆
epsilon
E
zeta
Z
eta
H
theta
Θ
iota
I
kappa
K
lambda
Λ
mu
M
nu
N
xi
Ξ
omicron
O
pi
Π
rho
P
sigma
Σ
tau
T
upsilon
Υ
phi
Φ
chi
X
psi
Ψ
omega
Ω
2
Lowercase
α
β
γ
δ
ζ
η
θ
ι
κ
λ
µ
ν
ξ
o
π
ρ
σ
τ
υ
φ
χ
ψ
ω