Mathematical and Scientific Symbols
|
+
|
plus
|
/'plʌs/
|
|
-
|
minus
|
/'maɪnəs/
|
|
±
|
plus or
minus
|
/'plʌs
ɔ: 'maɪnəs/
|
|
x
|
multiplied
by
|
/'mʌltɪplaɪd
baɪ/
|
|
/
|
over;
divided by
|
/'əʊvə/
/dɪ'vaɪdəd/
|
|
÷
|
divided
|
/dɪ'vaɪdəd/
|
|
=
|
equals
|
/'ɪ:kwəlz/
|
|
≈
|
approximately,
similar
|
/ə'prɒksɪmətlɪ/
/'sɪmɪlə tʊ/
|
|
≡
|
equivalent
to; identical
|
/ɪk'wɪvələnt
tʊ/ /aɪ'dentɪkl tʊ/
|
|
≠
|
not equal
to
|
/'nɒt
'iːkwəl tʊ/
|
|
>
|
greater
than
|
/'greɪtə
ðən/
|
|
<
|
less than
|
/'les ðən/
|
|
≥
|
greater
than or equal to
|
/'greɪtə
ðən ər 'iːkwəl tʊ/
|
|
≤
|
less than
or equal to
|
/'les
ðən ər' iːkwəl tʊ/
|
|
⊁
|
not
greater than
|
/'nɒt
'greɪtə ðən/
|
|
⊀
|
not less
than
|
/'nɒt 'les
ðən/
|
|
≫
|
much
greater than
|
/'mʌʧ
'greɪtə ðən/
|
|
≪
|
much less
than
|
/'mʌʧ 'les
ðən/
|
|
⊥
|
perpendicular
to
|
/pɜːpən'dɪkjʊlə
tʊ/
|
|
∣∣
|
parallel
to
|
/'pærəlel
tʊ/
|
|
≢
|
not
equivalent to, not identical to
|
/'nɒt
ɪk'wɪvələnt tʊ/ /'nɒt aɪ'dentɪkl tʊ/
|
|
≄≉
|
not
similar to
|
/'nɒt
'sɪmɪlə tʊ/
|
|
²
|
squared
|
/'skweəd/
|
|
³
|
cubed
|
/'kju:bd/
|
|
4
|
to the
fourth; to the power four
|
/tə ðə
'fɔːθ/ /te ðə 'pɑʊə fɔː/
|
|
n
|
to
the n; to the nth; to the power n
|
/tə ðɪ en;
tə dɪ enθ; tə ðə pɑʊər en/
|
|
√
|
root; square
root
|
/ru:t/
/skweə ru:t/
|
|
∛
|
cube root
|
/kju:b
ru:t/
|
|
∜
|
fourth
root
|
/fɔːθ
ruːt/
|
|
!
|
factorial
|
/fæk'tɔːrɪəl/
|
|
%
|
percent
|
/pə'sent/
|
|
∞
|
infinity
|
/ɪn'fɪnətɪ/
|
|
∝
|
varies
as; proportional to
|
/'vɛərɪz/
/prə'pɔːʃənəl/
|
|
˙
|
dot
|
/dɒt/
|
|
¨
|
double dot
|
/dʌbl dɒt/
|
|
:
|
is to,
ratio of
|
/reɪʃɪəʊ/
|
|
f(x) fx
|
f; function
|
/ef/
/'fʌŋkʃən/
|
|
f'(x)
|
f dash;
derivative
|
/dæʃ/
/dɪ'rɪvətɪv/
|
|
f''x
|
f double-dash; second
derivative
|
/'dʌbl
dæʃ/ /'sekənd dɪ'rɪvətɪv/
|
|
f'''(x)
|
f
triple-dash; f treble-dash; third derivative
|
/'trɪpl
dæʃ/ / trebl dæʃ/ /θɜ:d dɪ'rɪvətɪv/
|
|
f(4)
|
f
four; fourth derivative
|
/fɔːθ
dɪ'rɪvətɪv/
|
|
∂
|
partial
derivative, delta
|
/paːʃəl dɪ'rɪvətɪv/
/deltə/
|
|
∫
|
integral
|
/'ɪntɪgrəl/
|
|
∑
|
sum
|
/sʌm/
|
|
w.r.t.
|
with
respect to
|
/wɪð
'rɪspekt/
|
|
log
|
log
|
/lɒg/
|
|
log₂x
|
log to the
base 2 of x
|
/lɒg tə ðə
beɪs tu: əv eks/
|
|
∴
|
therefore
|
/'ðɛəfɔː/
|
|
∵
|
because
|
/bɪ'kɒz/
|
|
→
|
gives,
leads to, approaches
|
/gɪvz/ /li:dz
tʊ/ /əprəʊʧəz/
|
|
/
|
per
|
/pɜ:/
|
|
∈
|
belongs
to; a member of; an element of
|
/bɪ'lɒŋz/
/'membə/ /'elɪmənt/
|
|
∉
|
does not
belong to; is not a member of; is not an element of
|
/nɒt bɪ'lɒŋ/
/nɒt ə 'membə/ /nɒt ən 'elɪmənt/
|
|
⊂
|
contained
in; a proper subset of
|
/kən'teɪnd
ɪn/ /'prɒpə 'sʌbset/
|
|
⊆
|
contained
in; subset
|
/'sʌbset/
|
|
⋂
|
intersection
|
/'ɪntəsekʃən/
|
|
⋃
|
union
|
/'juːnɪən/
|
|
∀
|
for all
|
/fə rɔ:l/
|
|
cos x
|
cos x;
cosine x
|
/kɒz/
|
|
sin x
|
sine x
|
/saɪn/
|
|
tan x
|
tangent x
|
/tan/
|
|
cosec x
|
cosec x
|
/'kəʊsek/
|
|
sinh x
|
shine x
|
/'ʃaɪn/
|
|
cosh x
|
cosh x
|
/'kɒʃ/
|
|
tanh x
|
than x
|
/θæn/
|
|
|x|
|
mod x;
modulus x
|
/mɒd/
/'mɒdjʊləs/
|
|
℃
|
degrees
Centigrade
|
/dɪ'gri:z
'sentɪgreɪd/
|
|
℉
|
degrees
Fahrenheit
|
/dɪ'gri:z
'færənhaɪt/
|
|
°K
|
degrees
Kelvin
|
/dɪ'gri:z
'kelvɪn/
|
|
0°K,
–273.15 °C
|
absolute
zero
|
/absəlu:t
zi:rəʊ/
|
|
mm
|
millimetre
|
/'mɪlɪmiːtə/
|
|
cm
|
centimetre
|
/'sentɪmiːtə/
|
|
cc, cm³
|
cubic
centimetre, centimetre cubed
|
/'kjuːbɪk
'sentɪmiːtə/ /'sentɪmiːtə 'kju:bd/
|
|
m
|
metre
|
/'miːtə/
|
|
km
|
kilometre
|
/kɪ'lɒmɪtə/
|
|
mg
|
milligram
|
/'mɪlɪgræm/
|
|
g
|
gram
|
/græm/
|
|
kg
|
kilogram
|
/'kɪləgræm/
|
|
AC
|
A.C.
|
/eɪ si:/
|
|
DC
|
D.C.
|
/di: si:/
|
Examples
|
x + 1
|
x plus one
|
|
x -1
|
x minus
one
|
|
x ± 1
|
x plus or
minus one
|
|
xy
|
x y;
x times y; x multiplied by y
|
|
(x — y)(x
+ y)
|
x
minus y, x plus y
|
|
x/y
|
x over
y; x divided by y;
|
|
x ÷ y
|
x divided
by y
|
|
x = 5
|
x equals
5; x is equal to 5
|
|
x ≈ y
|
x is
approximately equal to y
|
|
x ≡ y
|
x is
equivalent to y; x is identical with y
|
|
x ≠ y
|
x is not
equal to y
|
|
x > y
|
x is
greater than y
|
|
x < y
|
x is
less than y
|
|
x ≥ y
|
x is
greater than or equal to y
|
|
x ≤ y
|
x is less
than or equal to y
|
|
0 < x
< 1
|
zero is
less than x is less than 1; x is greater than zero and less than 1
|
|
0 ≤
x ≤ 1
|
zero is
less than or equal to x is less than or equal to 1; x is greater than or
equal to zero and less than or equal to 1
|
|
x²
|
x squared
|
|
x³
|
x cubed
|
|
x4
|
x to the
fourth; x to the power four
|
|
xn
|
x to the
n; x to the nth; x to the power n
|
|
x-n
|
x to the
minus n; x to the power of minus n
|
|
√
|
root
x; square root x; the square root of x
|
|
∛
|
the cube
root of x
|
|
∜
|
the fourth
root of x
|
 |
the nth
root of x
|
|
(x + y)²
|
x plus y
all squared
|
|
(x/y)²
|
x over y
all squared
|
|
n!
|
n
factorial; factorial n
|
|
x%
|
x percent
|
|
∞
|
Infinity
|
|
x ∝ y
|
x varies
as y; x is (directly) proportional to y
|
|
x ∝ 1/y
|
x varies
as one over y; x is indirectly proportional to y
|
|
ẋ
|
x dot
|
|
ẍ
|
x double
dot
|
|
f(x) fx
|
f of x;
the function of x
|
|
f'(x)
|
f dash x;
the (first) derivative of with respect to x
|
|
f''x
|
f
double-dash x; the second derivative of f with respect to x
|
|
f'''(x)
|
f
triple-dash x; f treble-dash x; the third derivative of f with respect to x
|
|
f(4)
|
f four x;
the fourth derivative of f with respect to x
|
|
∂v
|
the
partial derivative of v
|
|
∂v
∂θ |
delta v by
delta theta, the partial derivative of v with respect to θ
|
|
∂²v
∂θ² |
delta two
v by delta theta squared; the second partial derivative of v with respect to
θ
|
|
dv
|
the
derivative of v
|
|
dv
dθ |
d v by d
theta, the derivative of v with respect to theta
|
|
d²v
dθ² |
d 2 v by d
theta squared, the second derivative of v with respect to theta,
|
|
∫
|
Integral
|
 |
integral from
zero to infinity
|
|
∑
|
Sum
|
 |
the sum
from i equals 1 to n
|
|
w.r.t.
|
with
respect to
|
|
logey
|
log to the
base e of y; log y to the base e; natural log (of) y
|
|
∴
|
Therefore
|
|
∵
|
Because
|
|
→
|
gives,
approaches
|
|
Δx → 0
|
delta x
approaches zero
|
|
lim
Δx→0 |
the limit
as delta x approaches zero, the limit as delta x tends to zero
|
|
Lt
Δx→0 |
the limit
as delta x approaches zero, the limit as delta x tends to zero
|
|
m/sec
|
metres per
second
|
|
x ∈ A
|
x belongs
to A; x is a member of A; x is an element of A
|
|
x∉ A
|
x does not
belong to A; x is not a member of A; x is not an element of A
|
|
A⊂ B
|
A is
contained in B; A is a proper subset of B
|
|
A ⊆ B
|
A is
contained in B; A is a subset of B
|
|
A ⋂ B
|
A
intersection B
|
|
A ⋃ B
|
A union B
|
|
cos x
|
cos x;
cosine x
|
|
sin x
|
sine x
|
|
tan x
|
tangent x,
tan x
|
|
cosec x
|
cosec x
|
|
sinh x
|
shine x
|
|
cosh x
|
cosh x
|
|
tanh x
|
than x
|
|
|x|
|
mod x;
modulus x
|
|
18 ℃
|
eighteen
degrees Centigrade
|
|
70 ℉
|
seventy
degrees Fahrenheit
|
Greek alphabet
|
Α
|
α
|
alpha
|
/'ælfə/
|
|
Β
|
β
|
beta
|
/'bi:tə/
|
|
Γ
|
γ
|
gamma
|
/'gæmə/
|
|
Δ
|
δ
|
delta
|
/'deltə/
|
|
Ε
|
ε
|
epsilon
|
/'epsilən/
|
|
Ζ
|
ζ
|
zeta
|
/'ziːtə/
|
|
Η
|
η
|
eta
|
/'iːtə/
|
|
Θ
|
θ
|
theta
|
/'θiːtə/
|
|
Ι
|
ι
|
iota
|
/aɪ'əʊtə/
|
|
Κ
|
κ
|
kappa
|
/'kæpə/
|
|
Λ
|
λ
|
lamda
|
/'læmdə/
|
|
Μ
|
μ
|
mu
|
/'mjuː/
|
|
Ν
|
ν
|
nu
|
/'njuː/
|
|
Ξ
|
ξ
|
xi
|
/'ksaɪ/
|
|
Ο
|
ο
|
omicron
|
/'əʊmɪkrən/
|
|
Π
|
π
|
pi
|
/'paɪ/
|
|
Ρ
|
ρς
|
rho
|
/'rəʊ/
|
|
Σ
|
σ
|
sigma
|
/'sɪgmə/
|
|
Τ
|
τ
|
tau
|
/'tɑʊ/
|
|
Υ
|
υ
|
upsilon
|
/'jʊpsɪlən/
|
|
Φ
|
φ
|
phi
|
/'faɪ/
|
|
Χ
|
χ
|
chi
|
/'kaɪ/
|
|
Ψ
|
ψ
|
psi
|
/'psaɪ/
|
|
Ω
|
ω
|
omega
|
/'əʊmɪgə/
|
Fractions
|
½
|
a half
|
/ə 'hɑ:f/
|
|
¼
|
a quarter
|
/ə
'kwɔːtə/
|
|
¾
|
three
quarters
|
/θriː
'kwɔːtəz/
|
|
⅓
|
a third
|
/ə 'θɜ:d/
|
|
⅔
|
two thirds
|
/tu:
'θɜ:dz/
|
|
⅕
|
a fifth
|
/ə 'fɪfθ/
|
|
⅖
|
two fifths
|
/tu:
'fɪfθs/
|
|
⅗
|
three
fifths
|
/θriː
'fɪfθs/
|
|
⅘
|
four
fifths
|
/fɔː
'fɪfθs/
|
|
⅙
|
a sixth
|
/ə 'sɪksθ/
|
|
⅚
|
five
sixths
|
/faɪv
'sɪksθs/
|
|
⅛
|
an eighth
|
/ən 'eɪtθ/
|
|
⅜
|
three eighths
|
/θriː
'eɪtθs/
|
|
⅝
|
five
eighths
|
/faɪv 'eɪtθs/
|
|
⅞
|
seven
eighths
|
/sevən 'eɪtθs/
|
Decimal Fractions
|
0.1
|
nought
point one
|
/nɔ:t
pɔɪnt wʌn/
|
|
0.01
|
nought
point oh one
|
/nɔ:t pɔɪnt
əʊ wʌn/
|
|
0.0001
|
nought
point oh oh oh one
|
/ten pɔɪnt
əʊ əʊ əʊ wʌn/
|
|
1.1
|
one point
one
|
/wʌn pɔɪnt wʌn/
|
|
1.2
|
one point
two
|
/wʌn pɔɪnt
tu:/
|
|
1.23
|
one point
two three
|
/wʌn pɔɪnt
tu: θri:/
|
|
1.0123
|
one point
oh one two three
|
/wʌn pɔɪnt
əʊ wʌn tu: θri:/
|
|
10.01
|
ten point
oh one
|
/ten pɔɪnt
əʊ wʌn/
|
|
21.57
|
twenty-one
point five seven
|
/'twentɪ
wʌn pɔɪnt faɪv 'sevən/
|
|
2.6666666666....
|
two point
six recurring
|
/tu: pɔɪnt
sɪks rɪ'kɜ:rɪŋ/
|
|
2.612361236123...
|
two point
six one two three recurring
|
/tu: pɔɪnt
sɪks wʌn tu: θri: rɪ'kɜ:rɪŋ/
|
|
2.5
million
|
two point
five million
|
/tu:
pɔɪnt faɪv 'mɪljən/
|
SI Units: Prefixes
|
10-24
|
yocto
|
y
|
/'jɒktəʊ/
|
|
10-21
|
zepto
|
z
|
/'zeptəʊ/
|
|
10-18
|
atto
|
a
|
/'atəʊ/
|
|
10-15
|
femto
|
f
|
/'femtəʊ/
|
|
10-12
|
pico
|
p
|
/'pi:kəʊ/
|
|
10-9
|
nano
|
n
|
/'nanəʊ/
|
|
10-6
|
micro
|
µ
|
/'maɪkrəʊ/
|
|
10-3
|
milli
|
m
|
/'mɪlɪ/
|
|
10-2
|
centi
|
c
|
/'sentɪ/
|
|
10-1
|
deci
|
d
|
/'desɪ/
|
|
103
|
kilo
|
k
|
/'kɪləʊ/
|
|
106
|
mega
|
M
|
/'megə/
|
|
109
|
giga
|
G
|
/'gɪgə/
|
|
1012
|
tera
|
T
|
/'terə/
|
|
1015
|
peta
|
P
|
/'petə/
|
|
1018
|
exa
|
E
|
/'eksə/
|
|
1021
|
zetta
|
Z
|
/'zetə/
|
|
1024
|
yotta
|
Y
|
/'jɒtə/
|
|
1027
|
xona
|
X
|
/'zəʊnə/
|
|
1030
|
weka
|
W
|
/'wekə/
|
|
1033
|
vunda
|
V
|
/'vʊndə/
|
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