04/29/2024
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Mathematical Symbols

Vincent Stefanetti010 mins
Symbol What it is How it is read How it is used Sample expression
+ Addition sign … plus … Sum of a few values 3 + 5 = 8
Logical OR symbol … or … Logical disjunction ¬(A + B) = ¬A * ¬B
* Multiplication sign … times … Product of two values 3 x 5 = 15
Logical AND symbol … and … Logical conjunction ¬(A * B) = ¬A + ¬B
x Multiplication sign … times … Product of two values 3 x 5 = 15
· Multiplication sign … times … Product of two values 3 · 5 = 15
summation sign The summation of … Sum of many or
infinitely many values
Integral sign The integral of … integration x2 dx = x3/3 + c
Double integral sign The double integral of … integration f(x,y) dx dy
Triple integral sign The triple integral of … integration f(x,y,z) dx dy dz
Line integral sign The line integral of … integration F dx
Surface integral sign The surface integral of … integration F(x,y,z) dx dy
– Subtraction sign … minus … Difference of two values, 3 – 5 = -2
Minus sign Negative… negative number
± Plus/minus sign … plus or minus … Expression of range, 500 kbps ± 10%
error, or tolerance
dot product sign … dot … Scalar (dot) product A B = B A
of two vectors
x Cross product sign … cross … Vector (cross) product A x B = – (B x A)
of two vectors
Product sign The product of … Product of three up to
infinitely many values
^ Carat … to the power of … exponent 2 ^ 5 = 32
! Exclamation … factorial Product of all positive 5! = 120
integers up to a
certain value
Surd … root of … Algebraic expressions z = (x + y)
Square root symbol The square root of … Algebraic expressions
… Continuation sign … and so on up to … Extension of sequence S = {1, 2, 3, …}
… and so on indefinitely
/ Slash … divided by … Division 3/4 = 0.75
… over …
÷ Division sign … divided by … Division 3 ÷ 4 = 0.75
Percent symbol … percent … Proportion 0.032 = 3.2
Per mil symbol … per mil … Proportion 0.032 = 32
: Colon, … is to … Division or ratio, 2:4 = 20:40
ratio sign … such that … symbol following x : x > 4 and x < 5
… it is true that … logical quantifier or
used in defining a set x : x < 0 or x > -1
S = {x : x < 3}
| Vertical line … such that … Symbol following x | x > 4 and x < 5
…it is true that … logical quantifier or
used in defining a set x | x < 0 or x > -1
S = {x | x < 3}
:: Double colon … averaged with … arithmetic mean 3 :: 11 = 7
lemniscate … infinity Infinite summations x : x <
… increases without limit Infinite sequence
Limit
( ) Parentheses …quantity… Denotes a quantity, list, (x + y) + z
…list… set of coordinates, or an (a1, a2, a3, a4)
…set of coordinates… open interval (x,y,z)
…open interval (3,5)
[ ] Square brackets … the quantity … Denotes a quantity or a w + [(x + y) + z]
… the closed interval … closed interval [3,5]
( ] Hybrid brackets … the half-open interval … Denotes a (3,5]
half-open interval
[ )

Hybrid brackets

… the half-open interval …

Denotes a

[3,5)

half-open interval

{ }

Curly brackets

… the quantity …

Denotes a quantity or a set

E = {2, 4, 6, 8, …}

… the set …

=

Equal sign

… equals …

Indicates two values

TRUE

are the same

2z2 +
4z – 6 = 0

<!–[if gte vml 1]>

 proportionalitysign … is proportional to … Indicates two variables x y
change in direct proportion
~ Similarity sign … is similar to … Indicates two objects are ABC ~ DEF
geometrically similar
Approximate … is approximately equal to … Indicates two values are x + y z
equal sign close to each other
Inequality sign … is not equal to … Indicates two values x y
are different
< Inequality sign … is less than … Indicates value on left 3 < 5
is smaller than x < y
value on right
Inequality sign … is less than or equal to … Indicates value on left x y
… is at most equal to … is smaller than or equal to
value on right
> Inequality sign … is greater than … Indicates value on left 5 > 3
is larger than x > y
value on right
Inequality sign … is greater than or equal to … Indicates value on left x y
is larger than or equal to
value on right
| | absolute valuesign The absolute value of … Distance of value from | -3 | = 3
origin in number line,
plane, or space
increment sign, the change in … Indicates a small change, m = y / x
Triangle symbol triangle … Denotes vertices of triangle ABC =
DEF
Perpendicularity … is perpendicular to … Geometry L M
symbol
// Parallel symbol … is parallel to … Geometry L // M
Angle symbol Angle … Geometry ABC = DEF
Existential quantifier For some … Logical statements x : x > 4 and x < 5
There exists a(n) …
Universal quantifier For all … Logical statements x : x < 0 or x > -1
For every …
¬ Logical negation not … Logical statements ¬(¬A) A
symbol
logical implication … implies … Logical statements A B
symbol If … then …
logical equivalence … is logically equivalent to … Logical statements A B
symbol … if and only if ..
Three dots … therefore … Logical statements or x = y and y = z
… it follows that … mathematical proofs x = z
Element-of … is an element of Sets a A
symbol a set …
Not-element-of … is not an element of Sets b A
symbol a set …
Subset symbol … is a subset of … Sets A B
Proper subset symbol … is a proper subset of … Sets A B
Union symbol … union … Sets A B = B A
Intersection symbol … intersect … Sets A B = B A
… intersected with …
Null symbol The null set Sets = { }
The empty set
Hebrew aleph Aleph … Transfinite cardinal 1 + 0 = 1
(uppercase)
º Degree symbol … degree(s) Angular measure = 45º
Temperature T = +20 ºC
Greek theta … theta … Angular variable = 90º
(lowercase)
Greek phi … phi … Angular variable = 45º
(lowercase)
Greek lambda … lambda … Wavelength = 70 cm
(lowercase) Ratio = 3:1
Eigenvalue
Lebesgue measure
µ Greek mu micro- (10-6) Prefix multiplier C = 0.001 µF
(lowercase)
Greek pi … pi … General science 3.14159
(lowercase)
Greek omega … omega … Volume of an object R2 = 330
(uppercase) Ohms (resistance)
Greek omega … omega … Transfinite ordinal = 36,000 rad/s
(lowercase) Angular velocity = 1/60 s
Period
, N Enhanced or bold N The set of natural numbers Number theory = {0, 1, 2, 3, …}
Set theory
, Z Enhanced or bold Z The set of integers Number theory = {0, 1, -1, 2, -2, 3, -3, …}
Set theory
, Q Enhanced or bold Q The set of rational numbers Number theory = {a/b | a and bare in }
Set theory
, R Enhanced or bold R The set of real numbers Number theory What is the cardinality of ?
Set theory

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