[A-LEVEL MATHS] Set Notation

is an element of

∈

is not an element of

∉

is a subset of

⊆

is a proper subset of

⊂

the set with elements x₁, x₂, ...

{x₁, x₂, ...}

the set of all x such that ...

{ x : ...}

the number of elements in set A

n(A)

the empty set

∅

the universal set

ε

the complement of the set A

A′

the set of natural numbers, {1, 2, 3, ...}

ℕ

the set of integers, {0, ±1, ±2, ±3, ...}

ℤ

the set of positive integers, {1, 2, 3, ...}

ℤ+

the set of non-negative integers, {0, 1, 2, 3, ...}

ℤ⁺₀

the set of real numbers

ℝ

ℚ

union

∪

intersection

∩

the ordered pair x, y

(x, y)

the closed interval {x ∈ ℝ: a ≤ x ≤ b}

[a, b]

the interval {x ∈ ℝ: a ≤ x < b}

[a, b)

the interval {{x ∈ ℝ: a < x ≤ b}

(a, b]

the open interval {x ∈ ℝ: a < x < b}

(a, b)

is proportional to

∝

p implies q (if p then q)

p⇒q

p is implied by q (if q then p)

p⇐q

p implies and is implied by q (p is equivalent to q)

p⇔ q

first term for an arithmetic or geometric sequence

a

last term for an arithmetic sequence

l

common difference for an arithmetic sequence

d

common ratio for a geometric sequence

r

sum to n terms of a sequence

Sₙ

sum to infinity of a sequence

S∞

a multiplied by b

a ⋅ b

a₁ + a₂ + ... + aₙ (definition)

a₁ x a₂ x ... x aₙ (definition)

the modulus of a

n factorial: n! = n × (n −1) × ...× 2 × 1, n∈ℕ; 0! = 1

n!

the value of the function f at 𝑥

f(𝑥)

the function f maps the element x to the element y

f : x|→y

the inverse function of the function f

f⁻¹

the composite function of f and g which is defined by

gf(𝑥) g(f(𝑥))

gf

the limit of f( ) x as x tends to a (def)

an increment of x

the nth derivative of y with respect to x

the first, second, ..., nth derivatives of f(𝑥) with

respect to x

f' (𝑥), fⁿ(𝑥), , f ⁽ⁿ⁾ (𝑥)

the first, second, ... derivatives of x with respect to t

the indefinite integral of y with respect to x

the definite integral of y with respect to x between the

limits x = a and x = b

base of natural logarithms

e

exponential function of x

logarithm to the base a of x

logₐ x

natural logarithm of x

the trigonometric functions

sin, cos, tan, cosec, sec, cot

the inverse trigonometric functions

radians

rad

the vector a

the vector represented in magnitude and direction by

the directed line segment AB

a unit vector in the direction of a

unit vectors in the directions of the cartesian

coordinate axes

the magnitude of a

column vector and corresponding unit vector notation

the magnitude of AB

position vector

r

displacement vector

s

velocity vector

v

acceleration vector

a

events

A,B,C, etc

complement of the event A

A′

probability of the event A conditional on the

event B

P(A | B)

random variables

X, Y, R, etc.

values of the random variables X, Y, R etc.

x, y, r, etc.

observations

x₁, x₂, ...

frequencies with which the observations x₁, x₂, ...

occur

f₁, f₂, ...

probability function of the discrete random

variable X

p(x), P(X = x)

probabilities of the values x₁, x₂, ... of the discrete

random variable X

p₁, p₂, ...

expectation of the random variable X

E(X)

variance of the random variable X

Var(X)

has the distribution

~

binomial distribution with parameters n and p, where n

is the number of trials and p is the probability of

success in a trial

B(n,p)

q =1− p for binomial distribution

q

Normal distribution with mean µ and variance σ2

N(µ, σ²)

standard Normal distribution

Z ~ N(0,1)

probability density function of the standardised Normal

variable with distribution N(0, 1)

φ

corresponding cumulative distribution function

Φ

population mean

µ

population variance

σ²

population standard deviation

σ

sample mean

sample variance

s²

sample standard deviation

s

Null hypothesis

H₀

Alternative hypothesis

H₁

product moment correlation coefficient for a sample

r

product moment correlation coefficient for a population

ρ

coefficient of friction

µ