Useful Mathematical Symbols

Aug 25, 2026

Upload by Noah

A reference-style compilation of commonly used mathematical symbols with concise guidance on what each symbol represents, how to pronounce or read it, and how it is applied in expressions. Entries cover logical operators, arithmetic and algebraic notation, summation and various integrals, vector operations, exponentiation and factorial-related forms, set and interval notation, quantifiers, inequality and absolute value, geometric relations, and Greek-letter symbols. Suitable for study and quick lookup when translating symbolic formulas into verbal meaning.

LanguageEnglish

CategoryExam

FormatPDF

Pages5

Reading Time13 min

AccessFree to download

Useful Mathematical Symbols

Logic and arithmetic symbols

Summation, integrals, and calculus notation

Algebra, exponents, and factorial-related forms

Sets, intervals, and quantifiers

Inequalities, absolute value, and relations

Geometry and vector operations

Greek letters and special symbols

32 Sutra: International Journal of Mathematical Science Education, Vol. 2, No. 1, 2009 Useful 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 2 + 6 = 8 ¬(A + B) = ¬A * ¬B Multiplication sign Logical AND symbol Multiplication sign Multiplication sign summation sign Integral sign double integral sign Triple integral sign Line integral sign Surface integral sign Subtraction sign Minus sign Plus/minus sign Dot product sign Cross product sign Product sign Carat ... times ... ... and ... ... times ... ... times ... The summation of ... The integral of ... The double integral of ... The triple integral of ... The line integral of ... The surface integral of ... ... minus ... Negative... ... plus or minus ... ... dot ... cross The product of ... ... to the power of ... Product of two values Logical conjunction Product of two values Product of two values Sum of many or infinitely many values integration integration integration integration integration Difference of two values, negative number Expression of range, error, or tolerance 2 x 6 = 12 ¬(A * B) = ¬A + ¬B 4 x 2 = 8 4 · 2 = 8 x2 dx = x3/3 + c f(x ,y) dx dy f(x,y,z) dx dy dz F dx F(x,y,z) dx dy 2-6 = -4 540 kbps ± 10% Scalar (dot) product A B = B A of two vectors Vector (cross) product A x B = - (B x A) of two vectors Product of three up to infinitely many values exponent 2 ^ 4 = 16 Sutra: International Journal of Mathematical Science Education, 33 Vol. 2 , No. 1, 2009 ! ... / ÷ % Exclamation surd square root symbol Continuation sign Slash Division sign Percent symbol Per mil symbol ... factoriall ... root of ... The square root of ... ... and so on up to ... ... and so on indefinitely ... divided by ... over ... divided by ... ... percent ... ... per mil ... Product of all positive integers up to a certain value Algebraic expressions Algebraic expressions Extension of sequence Division Division Proportion Proportion 3! = 6 z = (x + y) 4 = ±2 S = {1, 2, 3, ...} 3/4 = 0.75 3 ÷ 4 = 0.75 0.032 = 3.2 0.032 = 32 Colon, ratio sign Vertical line Double colon lemniscate Parentheses Square brackets Hybrid brackets Hybrid brackets Curly brackets ... is to ... ... such that ... ... it is true that ... ... such that ... ... it is true that ... ... averaged with ... ... infinity ... increases without limit ...quantity... ...list... ...set of coordinates......open interval ... the quantity ... ... the closed interval ... ... the half-open interval ... ... the half-open interval ... ... the quantity ... ... the set ... 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} 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} arithmetic mean Infinite summations Infinite sequence Limit 3 :: 11 = 7 ∀x : x < Denotes a quantity , list, set of coordinates, or an open interval (x + y) + z (a1 , a2, a3, a4) (x,y,z) (3,5) Denotes a quantity or a closed interval Denotes a half-open interval Denotes a half-open interval Denotes a quantity or a set w + [(x + y) + z] [2,4] (2,4][2,4) E = {2, 4, 6, 8, ...} 34 Sutra: International Journal of Mathematical Science Education, Vol. 2, No. 1, 2009 = Equal sign Proportionality sign ~ Similarity sign Approximate equal sign Inequality sign < Inequality sign Inequality sign > Inequality sign Inequality sign | | absolute value sign increment sign, Triangle symbol Perpendicularity symbol // Parallel

FAQs

What information does the symbol list provide for each mathematical symbol?

Each entry states what the symbol is, how it is read, and how it is used, often including a sample expression.

Which topics are covered besides basic arithmetic symbols?

The list includes logical operators, summation and multiple integrals, vector dot and cross products, exponents and factorial forms, and set/interval and quantifier notation.

How are sets and intervals represented in the document?

It provides symbols and readouts for elements, non-elements, subsets, proper subsets, union and intersection, null/empty set, and interval types such as open, closed, and half-open intervals.

Aug 25, 2026

Upload by Noah