Definition

# Mathematical Symbols

Contributor(s): Mark Bennett, Terry Stoltz, and Artemy Ustimenko

 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 = 45º T = +20 ºC Greek theta (lowercase) ... theta ... Angular variable = 90º Greek phi (lowercase) ... phi ... Angular variable = 45º 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 ?

This was first published in February 2006

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