Notation Flashcards
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 of A
A’
The set of natural numbers {1,2,3…} Positive integers
ℕ
The set of integers
Z
The set of positive integers
Z+
The set of non-negative integers
Z0+ (0 is subscript & + is superscript)
The set of real numbers
R
The set of rational numbers
Q
Union
U
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)
Because/since
∵
p implies q (if p then q)
p —> q
p is implied by q (if q then p)
p <— q
p implies & is implied by q (p is equivalent to q)
p ⇔ q
The first term of an arithmetic of geometric sequence
a
The last term of an arithmetic sequence
l
The common difference for an arithmetic sequence
d
The common ratio for a geometric sequence
r
Sum to n terms of a sequence
Sn
Sum to infinity of a sequence
S∞
a1 + a2 + a3… + an
n
Σ ai
i = 1
a1 x a2 x a3 x … x an
n
∏ ai
i = 1
n!
n factorial
0!
=1
Modulus of a
IaI
The binomial coefficient
n C r
Other way of writing the binomial coefficient
n! / r!(n - r)! Where r =< n & r is 0 or a positive integer
The other other binomial coefficient
n
r all in brackets
The function of f maps the element x to the element y
f : x —> y
The inverse 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
lim f(x)
x—> a
The increment of x
∆x, δx
The derivative of y with respect to x
dy
—
dx
The nth derivative of y with respect to x
d^ny
——
dx^n
The first, second; nth derivatives of f(x) with respect to x
f’(x), f’’(x) ; f^(n) (x)
The first and second derivatives of x with respect to t
. ..
x, x
The indefinite integral of y with respect to x
∫y dx
The definite integral of y with respect to x between the limits of x=a and x= b
a
∫ y dx
b
The base of natural logarithms
e
The exponential function of x
e^x, exp x
log x
a
Logarithm to the base a of x
Natural logarithm of x
ln x, log x
e
The trig functions
sin, cos, tan, cosec, sec & cot
Inverse trig functions
sin^-1, cos^-1, tan^-1, arcsin, arccos, arctan
rad
Radians
The vector a
a, a , a
— ~
The vector represented in magnitude and direction by the line segment AB
—>
AB
Unit vector in the direction of a
a
The magnitude of a
|a|, a
The magnitude of —>
AB
|—>|
|AB |, AB
Column vector and corresponding unit vector notation
(a) , ai + bj
(b)
Position vector
r
Displacement vector
s
Velocity vector
v
Acceleration vector
a
The union of events A & B
A ∪ B
The intersection of events A and B
A ∩ B
Complement if 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 variable X, Y, R, etc.
x, y, r, etc.
Values of 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 the parameters n & p, where n is the number of trials & p is the probability of success in a trial
B(n,p)
q
q= 1– p for binomial distribution
Normal distribution with mean μ and variance σ^2
N(μ, σ^2)
Standard Normal distribution
Z ~ N(0,1)
The probability density function of the standardised normal variable with the distribution N(0,1)
φ
Corresponding cumulative distribution function
Φ
Population mean
μ
Population variance
σ^2
Population standard deviation
σ
Sample mean
-
x
Sample variance
s^2
Sample standard deviation
s
Null hypothesis
H
0
Alternative hypothesis
H
1
Product moment correlation coefficient for a sample
r
Product moment correlation coefficient for a population
ρ
Displacement
S
Initial velocity
u
Velocity or final velocity
v
Acceleration due to gravity
a
Coefficient of friction
μ
