Mathematical Symbols

Symbol What it is How it is read How it is used Sample expression + Addition sign
Logical OR symbol … plus …
… or … Sum of a few values
Logical disjunction 3 + 5 = 8
¬(A + B) = ¬A * ¬B * Multiplication sign
Logical AND symbol … times …
… and … Product of two values
Logical conjunction 3 x 5 = 15
¬(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 sign … minus …
Negative… Difference of two values,
negative number 3 – 5 = -2 ± Plus/minus sign … plus or minus … Expression of range,
error, or tolerance 500 kbps ± 10% dot product sign … dot … Scalar (dot) product
of two vectors A B = B A x Cross product sign … cross … Vector (cross) product
of two vectors A x B = – (B x A) 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
integers up to a
certain value 5! = 120 Surd … root of … Algebraic expressions z = (x + y) Square root symbol The square root of … Algebraic expressions … Continuation sign … and so on up to …
… and so on indefinitely Extension of sequence S = {1, 2, 3, …} / Slash … divided by …
… over … Division 3/4 = 0.75 ÷ 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,
ratio sign … is to …
… such that …
… it is true that … Division or ratio,
symbol following
logical quantifier or
used in defining a set 2:4 = 20:40 x : x > 4 and x < 5 x : x < 0 or x > -1 S = { x : x < 3 } | Vertical line … such that …
…it is true that … Symbol following
logical quantifier or
used in defining a set x | x > 4 and x < 5 x | x < 0 or x > -1

S = { x | x < 3 } :: Double colon … averaged with … arithmetic mean 3 :: 11 = 7 lemniscate … infinity
… increases without limit Infinite summations
Infinite sequence
Limit x : x <  (  ) Parentheses …quantity…
…list…
…set of coordinates…
…open interval Denotes a quantity, list,
set of coordinates, or an
open interval (x + y) + z
(a1, a2, a3, a4)
(x,y,z)
(3,5) [  ] Square brackets … the quantity …
… the closed interval … Denotes a quantity or a
closed interval w + [(x + y) + z] [3,5] (  ] Hybrid brackets … the half-open interval … Denotes a
half-open interval (3,5] [  ) Hybrid brackets … the half-open interval … Denotes a
half-open interval [3,5) {  } Curly brackets … the quantity …
… the SET … Denotes a quantity or a SET E = {2, 4, 6, 8, …} = Equal sign … equals … Indicates two values
are the same -(-5) = 5
2z2 + 4z – 6 = 0 proportionality sign … is proportional to … Indicates two variables
change in direct proportion x  y ~ Similarity sign … is similar to … Indicates two objects are
geometrically similar ABC ~ DEF Approximate
equal sign … is approximately equal to … Indicates two values are
close to each other x + y  z Inequality sign … is not equal to … Indicates two values
are different x  y < Inequality sign … is less than … Indicates value on left
is smaller than
value on right 3 < 5
x < y Inequality sign … is less than or equal to …
… is at most equal to … Indicates value on left
is smaller than or equal to
value on right x y > Inequality sign … is greater than … Indicates value on left
is larger than
value on right 5 > 3
x > y ≥ Inequality sign … is greater than or equal to … Indicates value on left
is larger than or equal to
value on right x ≥ y |  | absolute value sign The absolute value of … Distance of value from
origin in number line,
plane, or space | -3 | = 3 increment sign,
Triangle symbol the change in …
triangle … Indicates a small change,
Denotes vertices of triangle m = y / x
ABC = DEF Perpendicularity
symbol … is perpendicular to … Geometry L M // Parallel symbol … is parallel to … Geometry L // M Angle symbol Angle … Geometry ABC = DEF Existential quantifier For some …
There exists a(n) … Logical statements x : x > 4 and x < 5 Universal quantifier For all …
For every … Logical statements x : x < 0 or x > -1 ¬ Logical negation
symbol not … Logical statements ¬(¬A) A logical implication
symbol … implies …
If … then … Logical statements A B logical equivalence
symbol … is logically equivalent to …
… if and only if .. Logical statements A B Three dots … therefore …
… it follows that … Logical statements or
mathematical proofs x = y and y = z
x = z Element-of
symbol … is an element of
a set … Sets a A Not-element-of
symbol … is not an element of
a set … Sets b A 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 …
… intersected with … Sets A B = B A Null symbol The null set
The empty set Sets = { } Hebrew aleph
(uppercase) Aleph … Transfinite cardinal 1 + 0 = 1 º Degree symbol … degree(s) Angular measure
Temperature T = +20 ºC  θ Greek theta
(lowercase) … theta … Angular variable  θ = 90º φ Greek phi
(lowercase) … phi … Angular variable = 45º λ Greek lambda
(lowercase) … lambda … Wavelength
Ratio
Eigenvalue
Lebesgue measure = 70 cm
= 3:1 µ Greek mu
(lowercase) micro- (10-6) Prefix multiplier C = 0.001 µF Greek pi
(lowercase) … pi … General science   3.14159 Greek omega
(uppercase) … omega … Volume of an object
Ohms (resistance) R2 = 330 Greek omega
(lowercase) … omega … Transfinite ordinal
Angular velocity
Period = 36,000 rad/s
= 1/60 s , N Enhanced or bold N The set of natural numbers Number theory
Set theory = {0, 1, 2, 3, …} , Z Enhanced or bold Z The set of integers Number theory
Set theory = {0, 1, -1, 2, -2, 3, -3, …} , Q Enhanced or bold Q The set of rational numbers Number theory
Set theory = {a/b | a and b are in } , R Enhanced or bold R The set of real numbers Number theory
Set theory What is the cardinality of ?