How to read some math formulae
APPENDIX
No. Symbols
How to read
+
Plus sign
-
Minus sign
±
Plus or minus
x
Multiplication sign
÷
Division sign
( )
Round bracket
[ ]
Square bracket
{ }
Curly bracket
Equivalent, similar
Is congruent to ../ Is isomorphic to

Rightward arrow

Leftward arrow

Left right arrow
%
Percent sign
‘
Apostrophe
(
Left parenthesis
)
Right parenthesis

Is Congruent to/ identical to
:
Colon
;
semicolon
English for mathematics
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How to read some math formulae
[
Left square bracket
]
Right square bracket\
≠
not equal to
/
Solidus

Integral

Intersection
{
Left curly bracket
}
Right curly bracket
 
Alpha is equal to beta/ Alpha equals beta
 / 
Positive infinity / Negative infinity

Alpha is not equal to Beta
 
Alpha is approximately equal to Beta
a>b
a is greater than b
a<b
a is less than b
a
b
a is substantially greater than b
a
b
a is substantially less than b
ab
a is greater than or equal to b
ab
a is less than or equal to b
1
alpha first / alpha sub one / alpha suffix one
2
Alpha second / alpha sub two / alpha suffix two
n
Alpha n-th
x 
x tends to infinity
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How to read some math formulae
x
x approaches infinity
a+b=c
a plus b equals c/ a plus b makes c / a plus b is c
( a  b) 2
a plus b all squared
a–b=c
a subtracts b equals c / a minus b leaves c
2x2=4
Twice two is four
5 x 5 = 25
Five times five is twenty five
1
2
a half / one half
1
3
a third / one third
1
4
A fourth/ a quarter
3
4
Three fourth / three quarters
2
1
2
Two and a half
3
4
3
Three and four quarters
0.5
Zero point five. / ou point five/ nought point five
0.002
Zero point two noughts two / Zero point zero zero two.
1.12
One point one two
0.000 0006
Zero point six noughts six
15.505
Fifteen point five ou five
x2
x square/ x squared/ the square of x / the second power of x /
x to the second power / x raised to the second power.
x3
x cube / x cubed / x raised to the third power
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How to read some math formulae
xn
x to nth power.
xn
x to the minus nth power.
x
The square root of x
3
x2
The cube root of x squared
n
x
The n-th root of x
a
(or a ÷ b)
b
The ratio of a to b
a:b=c:d
a is to b as c is to d
log 2 8  3
the logarithm of 8 with base 2 is 3
ln 10
the natural logarithm of 10
log100 = 2
A common logarithm” of 100 is 2
x A
x belongs to A/ x is the element of A
A B
A is the subset of B
A B
A is the proper subset of B
A B
The intersection of sets A and B
A B
The union of sets A and B.
AxB
Cartesian product of A and B

Empty set
{x| P(x)}
Set of all element x with the property P(x).
'
 prime
 ''
 double prime,  second prime
 "'
 triple prime
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How to read some math formulae

.
The mean value of 
The first derivative of x
x
..
The second derivative of x
x
...
x
The third derivative of x
Sup A
Supermum of A
Inf A
Infimum of A
a  b(mod m)
a and b are congruent modulo m
a:b
a divides b
Det A
Determinant of a square matrix A
Tr A
Trace of a square matrix A
AT
Transpose of a square matrix A
In
Unit matrix of degree n
M/N
Quotation space of an algebraic system M by N
Dim M
Dimension of a linear space M
Imf
Image of a mapping f
Kerf
Kernel of a mapping f
Coimf
Coimage of a mapping f
Cokerf
Cokernel of a mapping f
(a, b)
Inner product of two vector a and b
M N
Tensor product of two module M and N
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How to read some math formulae
f : X Y
Mapping f from X to Y
f |A
Restriction a mapping f to A
f g
Composite of mapping f and g
(a, b)
Open interval from a to b
[ a, b]
Close interval from a to b
(a , b]; [a, b)
Half – open – interval
Max A
Maximum of A
Min A
Minimum of A
1
 first,  sub one,  suffix one
2
 second,  sub two,  suffix two
n
 n-th,  sub n,  suffix n
f c'
f prime sub c, f prime suffix c, f suffix c prime
 2"
 second double prime,  double prime second
900
Ninety degree
6’
Six minutes
10’’
Ten seconds
90010 '6 ''
Ninety degree, six minutes, ten seconds
a+b=c
a plus b is c/ a plus b equals c/ a plus b is equal to c/ a plus b
makes c
   
 plus  all squared
2
a–b=c
a minus b is c/ a minus b leaves c
(2x – y)
Open bracket two times x minus y close bracket
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How to read some math formulae
2x2=4
Twice two is four / two times two is four
5 x 5 = 25
Five times five is twenty five/ five multiplied by five equals
twenty five.


S
S is equal to the ratio of  and 
   :
 divided by  is  /  divided by  equals 
a c

b d
The ratio of a to b equals the ratio of c to d. / a to b is as c to d
x  x2  y 2
y
x plus or minus square root of x square minus y square all over
y
df
dx
df over dx/ the first derivative of f with respect to x
The second derivative of f with respect to x
d (df )
 dx 
2
2 f
 x 
2

2 f
 y 
2
0
y = f(x)
b
Partial  two f over partial  x square plus partial  two f over
partial  y square equals zero.
y is a function of x
The integral from a to b/ integral between two limits a and b

a
x
d
Fdx
dx x0
E
P1

d over dx of the integral from x0 to x of capital Fdx
Capital E is equal to the ratio of the product P1 to the product

  cd

  cd
 plus  over  minus  equals c plus d over c minus d
V  u sin 2   cos2 
V equals u square root of sin square  minus cosine square 
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How to read some math formulae
c3  log c d
c cubed is equal to the logarithm of d to the base c
x, F ( x)
For all x: F(x) holds
x , F ( x )
There exists an x such that F(x) holds
A&B
A and B (conjunction)
A B
A or B (disjunction)
A B
A implies B (Implication)
Notices:
-
Let f denote…: Giả sử f là / Gọi f là
-
Let x be…: Cho x là… / Gọi x là …
-
Hence… Suy ra/ Do đó
-
In this way we obtain that … : Trong trường hợp này ta được
- For simplicity of notation, we write f instead of …: Để cho đơn giản trong ký hiệu,
chúng ta viết f thay cho …
-
For abbreviation, we let f stand for…: Để đơn giản, chúng ta gọi f là …
- We will write it simply x when no confusion can arise…: Chúng ta có thể viết một
cách đơn giản là x khi không có sự nhầm lẫn nào có thể xảy ra…
- Without loss of generality we can assume…./ There is no loss of generally in
assuming… : Không mất tính tổng quát có thể giả sử rằng..
-
By choosing b = a, we may assume that….: bằng cách chọn b = a, chúng ta được
- From now on we regard f as a map from …: từ đây trở đi chúng ta gọi f là ánh xạ
từ ….
-
We have proved….: Chúng ta vừa chứng minh được …
-
If … and if …. Then …. : Nếu … và nếu …. Thì …..
-
Suppose that … Then …./ Assume that … then …./ Write ….then…. : Giả sử rằng
….thì …..
-
Let P satisfy the hypotheses of … , then…: Giả sử P thỏa giả thiết của …. Thì ….
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How to read some math formulae
-
Futhermore ….: Hơn thế
-
In fact, …: Thật ra
-
Accordingly,….: Vì vậy, ….
-
On the contrary, …., suppose that…./ Conversely ….suppose that ….. : Ngược lại,
…..giả sử rằng…..
-
Assume (5) to hold for k, we will prove it for k + 1: Giả sử (5) đúng với giá trị k,
ta sẽ chứng minh nó đúng với k + 1.
-
We give the proof only for the case n = 3, other cases are left to the reader: Chúng
tôi chứng minh cho trường hợp n = 3, các trường hợp khác độc giả tự chứng minh.
-
The proof will be divided into 3 steps: Chứng minh được chia làm 3 phần.
-
Since … , we have …: vì …/ ta có ….
-
From (5) , we obtain: Từ (5) , ta có …
-
According to the above remark, we have M = N: Từ nhận xét trên ta có M = N.
-
Similar arguments apply to the case…: Lập luận tương tự cho trường hợp ….
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