Notation Flashcards
(103 cards)
1
Q
Is an element of
A
∈
2
Q
Is not an element of
A
∉
3
Q
Is a subset of
A
⊆
4
Q
Is a proper subset of
A
⊂
5
Q
The set with elements x1, x2…
A
{x1, x2…}
6
Q
The set of all x such that
A
{x:…}
7
Q
The number of elements in set a
A
n(A)
8
Q
The empty set
A
∅ = { }
9
Q
The universal set
A
ε
10
Q
The complement of the set of A
A
A’
11
Q
The set of natural numbers {1,2,3…} Positive integers
A
ℕ
12
Q
The set of integers
A
Z
13
Q
The set of positive integers
A
Z+
14
Q
The set of non-negative integers
A
Z0+ (0 is subscript & + is superscript)
15
Q
The set of real numbers
A
R
16
Q
The set of rational numbers
A
Q
17
Q
Union
A
U
18
Q
Intersection
A
∩
19
Q
The ordered pair x,y
A
(x,y)
20
Q
The closed interval {x ∈ R: a=< x =< b}
A
[a,b]
21
Q
The interval { x ∈ R: a=< x< b}
A
[a, b)
22
Q
The interval {x ∈ R: a < x =< b}
A
(a,b]
23
Q
The open interval {x ∈ R: a < x < b}
A
(a,b)
24
Q
Because/since
A
∵
25
p implies q (if p then q)
p —> q
26
p is implied by q (if q then p)
p <— q
27
p implies & is implied by q (p is equivalent to q)
p ⇔ q
28
The first term of an arithmetic of geometric sequence
a
29
The last term of an arithmetic sequence
l
30
The common difference for an arithmetic sequence
d
31
The common ratio for a geometric sequence
r
32
Sum to n terms of a sequence
Sn
33
Sum to infinity of a sequence
S∞
34
a1 + a2 + a3… + an
n
Σ ai
i = 1
35
a1 x a2 x a3 x … x an
n
∏ ai
i = 1
36
n!
n factorial
37
0!
=1
38
Modulus of a
IaI
39
The binomial coefficient
n C r
40
Other way of writing the binomial coefficient
n! / r!(n - r)! Where r =< n & r is 0 or a positive integer
41
The other other binomial coefficient
n
r all in brackets
42
The function of f maps the element x to the element y
f : x —> y
43
The inverse of the function f
f-1
44
The composite function of f and g which is defined by gf(x)= g(f(x))
gf
45
The limit of f(x) as x tends to a
lim f(x)
x—> a
46
The increment of x
∆x, δx
47
The derivative of y with respect to x
dy
—
dx
48
The nth derivative of y with respect to x
d^ny
——
dx^n
49
The first, second; nth derivatives of f(x) with respect to x
f’(x), f’’(x) ; f^(n) (x)
50
The first and second derivatives of x with respect to t
. ..
x, x
51
The indefinite integral of y with respect to x
∫y dx
52
The definite integral of y with respect to x between the limits of x=a and x= b
a
∫ y dx
b
53
The base of natural logarithms
e
54
The exponential function of x
e^x, exp x
55
log x
a
Logarithm to the base a of x
56
Natural logarithm of x
ln x, log x
e
57
The trig functions
sin, cos, tan, cosec, sec & cot
58
Inverse trig functions
sin^-1, cos^-1, tan^-1, arcsin, arccos, arctan
59
rad
Radians
60
The vector a
**a**, a , a
— ~
61
The vector represented in magnitude and direction by the line segment AB
—>
AB
62
Unit vector in the direction of a
^
a
63
The magnitude of a
|**a**|, a
64
The magnitude of —>
AB
|—>|
|AB |, AB
65
Column vector and corresponding unit vector notation
(a) , a**i** + b**j**
(b)
66
Position vector
**r**
67
Displacement vector
**s**
68
Velocity vector
**v**
69
Acceleration vector
**a**
70
The union of events A & B
A ∪ B
71
The intersection of events A and B
A ∩ B
72
Complement if the event A
A’
73
Probability of the event A conditional on the event B
P(A|B)
74
Random variables
X, Y, R, etc.
75
Values of the random variable X, Y, R, etc.
x, y, r, etc.
76
Values of observations
x1, x2, …
77
Frequencies with which the observations x1, x2, … occur
f1, f2
78
Probability function of the discrete random variable x
p(x), P(X=x)
79
Probabilities of the values x1, x2, … of the discrete random variable X
p1, p2, …
80
Expectation of the random variable X
E(X)
81
Variance of the random variable X
Var(X)
82
~
Has the distribution
83
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)
84
q
q= 1– p for binomial distribution
85
Normal distribution with mean μ and variance σ^2
N(μ, σ^2)
86
Standard Normal distribution
Z ~ N(0,1)
87
The probability density function of the standardised normal variable with the distribution N(0,1)
φ
88
Corresponding cumulative distribution function
Φ
89
Population mean
μ
90
Population variance
σ^2
91
Population standard deviation
σ
92
Sample mean
-
x
93
Sample variance
s^2
94
Sample standard deviation
s
95
Null hypothesis
H
0
96
Alternative hypothesis
H
1
97
Product moment correlation coefficient for a sample
r
98
Product moment correlation coefficient for a population
ρ
99
Displacement
S
100
Initial velocity
u
101
Velocity or final velocity
v
102
Acceleration due to gravity
a
103
Coefficient of friction
μ
