what does this symbol mean?

Math symbols

The signs of arithmetic and comparison, from greater than to the square root, what each one means and how it is read.

Math symbols are the signs of comparison and arithmetic, and two more: the integral sign of calculus and the therefore sign. Each sign’s page says what it means and how it is read aloud, gives its Unicode code point and name, lists the characters it is mistaken for, and names the first writer known to have used it where the histories name one. Most of the readings are from OpenStax’s free textbooks, published by Rice University. The dates come from Jeff Miller’s Earliest Uses of Various Mathematical Symbols, published by the University of St Andrews, and Florian Cajori’s A History of Mathematical Notations.

Comparison 7 symbols

Arithmetic 4 symbols

Beyond arithmetic 2 symbols

Signs that compare

OpenStax’s Prealgebra reads > as “is greater than”, so a > b is “a is greater than b”, and < as “is less than”. To tell the two apart it gives one rule: the smaller side of the sign faces the smaller number. A line under either sign adds “or equal”, making ≥ and ≤, and OpenStax’s Elementary Algebra gives “at least” as another way of saying ≥. = is read “is equal to”, and with a slash through it, ≠ is “is not equal to”. ≈ is read “approximately”, as in π ≈ 3.14 for pi.

Signs of arithmetic

± is read “plus or minus”. In the quadratic formula it gives two answers at once; in a measurement it gives the margin either side of a value, as when OpenStax’s Chemistry weighs a quarter at about 6.72 grams, ± 0.01 gram. × is read “times”, and OpenStax lists a dot (·) and brackets as other ways to write it. ÷ is read “divided by”, and Unicode gives it a second name, obelus. OpenStax calls √ the radical sign and the number under it the radicand, and reads √m as “the square root of m”.

Beyond arithmetic

The integral sign ∫ is a long S, for summa, and OpenStax’s Calculus notes that it suggests sigma, or summation. The therefore sign ∴ is three dots; Unicode names it THEREFORE and gives it a partner, ∵, named BECAUSE.

Look-alikes

Unicode’s code charts cross-refer several of these signs to characters that share their shape. × is a different character from the letter x. √ is paired with the check mark ✓, ∫ with the letter esh, ʃ, and ∴ with ⛬, HISTORIC SITE, one of the map symbols of the ARIB STD B24 standard. The n-ary product ∏ and n-ary summation ∑ are paired with the capital Greek letters Π and Σ. Unicode’s names can mislead: ≈ is ALMOST EQUAL TO, and the character named APPROXIMATELY EQUAL TO is ≅.

Where the signs came from

√ first appeared in Christoff Rudolff’s Die Coss, in 1525. Robert Recorde introduced = in The Whetstone of Witte in 1557, choosing two parallel lines “bicause noe 2, thynges, can be moare equalle”. > and < first appear in Thomas Harriot’s algebra, published in 1631, ten years after his death. William Oughtred used × and ± in his Clavis mathematicae, also published in 1631. Johann Rahn’s Teutsche Algebra of 1659 was the first book to use ÷ for division and to print ∴. Gottfried Wilhelm Leibniz first wrote ∫ on 29 October 1675, in an unpublished manuscript.

Differences by country

Cajori wrote in 1928 that ÷ for division belonged to Great Britain, the British dominions and the United States, and the colon to Continental Europe and Latin America. NIST’s guide to the SI prefers × for multiplying numbers where the decimal marker is a dot, as in the United States, and the half-high dot where it is a comma.

Sources

  1. Prealgebra 2e, 2.1 Use the Language of Algebra, OpenStax (Rice University), Inequality; Table 2.2; Equality Symbol
  2. Elementary Algebra 2e, 2.7 Solve Linear Inequalities, OpenStax (Rice University), Translate to an Inequality and Solve; Table 2.7
  3. Prealgebra 2e, 5.3 Decimals and Fractions, OpenStax (Rice University), Properties of Circles; Example 5.36
  4. Prealgebra 2e, 5.7 Simplify and Use Square Roots, OpenStax (Rice University), Approximate Square Roots; Use Square Root Notation
  5. Intermediate Algebra 2e, 9.3 Solve Quadratic Equations Using the Quadratic Formula, OpenStax (Rice University), Solve Quadratic Equations Using the Quadratic Formula
  6. Chemistry 2e, 1.5 Measurement Uncertainty, Accuracy, and Precision, OpenStax (Rice University), Measurement uncertainty
  7. Prealgebra 2e, 1.4 Multiply Whole Numbers, OpenStax (Rice University), Operation Symbols for Multiplication
  8. Prealgebra 2e, 1.5 Divide Whole Numbers, OpenStax (Rice University), Operation Symbols for Division
  9. Calculus Volume 1, 5.2 The Definite Integral, OpenStax (Rice University), Definition and Notation
  10. C1 Controls and Latin-1 Supplement (code chart, Range 0080–00FF), The Unicode Standard, Version 18.0, Unicode Consortium, Latin-1 Supplement, 00D7; Latin-1 Supplement, 00F7
  11. Mathematical Operators: Range 2200–22FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Mathematical Operators, 221A–221C; Mathematical Operators, 222B–222E; Mathematical Operators, 2234–2235; Mathematical Operators, 2243–2248; N-ary operators
  12. Miscellaneous Symbols, Range: 2600–26FF (code chart), The Unicode Standard, Unicode Consortium, Miscellaneous Symbols, 26EC
  13. Earliest Uses of Symbols of Relation, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Less than and greater than; Equality
  14. Earliest Uses of Symbols of Operation, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Square root; Multiplication symbols; Other symbols of operation; Division symbols; Order of operations
  15. Earliest Uses of Symbols of Calculus, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Integral; Infinity
  16. Earliest Uses of Symbols of Set Theory and Logic, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Therefore and because
  17. A History of Mathematical Notations, Vol. I: Notations in Elementary Mathematics, Florian Cajori (Chicago: Open Court, 1928); full text of the Wellcome Collection copy, Internet Archive, §§ 237, 240
  18. Guide for the Use of the International System of Units (SI), NIST Special Publication 811 (2008), National Institute of Standards and Technology, Secs. 7.7, 10.5.4

Last reviewed September 30, 2026 by Rory Hansen. How we research