Table of mathematical symbols by introduction date
The following table lists many specialized symbols commonly used in mathematics, ordered by their introduction date.
Symbol |
Name | Date of earliest use | First author to use |
|---|---|---|---|
+ |
plus sign | ca. 1360 (abbreviation for Latin et resembling the plus sign) | Nicole Oresme |
− |
minus sign | 1489 (first appearance of minus sign, and also first appearance of plus sign in print) | Johannes Widmann |
√ |
radical symbol (for square root) | 1525 (without the vinculum above the radicand) | Christoff Rudolff |
(…) |
parentheses (for precedence grouping) | 1544 (in handwritten notes) | Michael Stifel |
| 1556 | Niccolò Tartaglia | ||
= |
equals sign | 1557 | Robert Recorde |
× |
multiplication sign | 1618 | William Oughtred |
± |
plus-minus sign | 1628 | |
∷ |
proportion sign | ||
n√ |
radical symbol (for nth root) | 1629 | Albert Girard |
< > |
strict inequality signs (less-than sign and greater-than sign) | 1631 | Thomas Harriot |
xy |
superscript notation (for exponentiation) | 1636 (using Roman numerals as superscripts) | James Hume |
| 1637 (in the modern form) | René Descartes | ||
√ ̅ |
radical symbol (for square root) | 1637 (with the vinculum above the radicand) | René Descartes |
% |
percent sign | ca. 1650 | unknown |
÷ |
division sign (a.k.a. obelus) | 1659 | Johann Rahn |
∞ |
infinity sign | 1655 | John Wallis |
≤ ≥ |
unstrict inequality signs (less-than or equals to sign and greater-than or equals to sign) | 1670 (with the horizontal bar over the inequality sign, rather than below it) | |
| 1734 (with double horizontal bar below the inequality sign) | Pierre Bouguer | ||
d |
differential sign | 1675 | Gottfried Leibniz |
∫ |
integral sign | ||
: |
colon (for division) | 1684 (deriving from use of colon to denote fractions, dating back to 1633) | |
· |
middle dot (for multiplication) | 1698 (perhaps deriving from a much earlier use of middle dot to separate juxtaposed numbers) | |
⁄ |
division slash (a.k.a. solidus) | 1718 (deriving from horizontal fraction bar, invented by Arabs in the 12th century) | Thomas Twining |
≠ |
inequality sign (not equal to) | unknown | Leonhard Euler |
∑ |
summation symbol | 1755 | |
∝ |
proportionality sign | 1768 | William Emerson |
∂ |
partial differential sign (a.k.a. curly d or Jacobi's delta) | 1770 | Marquis de Condorcet |
x′ |
prime symbol (for derivative) | Joseph Louis Lagrange | |
≡ |
identity sign (for congruence relation) | 1801 (first appearance in print; used previously in personal writings of Gauss) | Carl Friedrich Gauss |
[x] |
integral part (a.k.a. floor) | 1808 | |
∏ |
product symbol | 1812 | |
! |
factorial | 1808 | Christian Kramp |
⊂ ⊃ |
set inclusion signs (subset of, superset of) | 1817 | Joseph Gergonne |
| 1890 | Ernst Schröder | ||
|…| |
absolute value notation | 1841 | Karl Weierstrass |
| determinant of a matrix | Arthur Cayley | ||
‖…‖ |
matrix notation | 1843[1] | |
∇ |
nabla symbol (for vector differential) | 1846 (previously used by Hamilton as a general-purpose operator sign) | William Rowan Hamilton |
∩ ∪ |
intersection union |
1888 | Giuseppe Peano |
∈ |
membership sign (is an element of) | 1894 | |
∃ |
existential quantifier (there exists) | 1897 | |
ℵ |
aleph symbol (for transfinite cardinal numbers) | 1893 | Georg Cantor |
{…} |
braces, a.k.a. curly brackets (for set notation) | 1895 | |
ℕ |
Blackboard bold capital N (for natural numbers set) | Giuseppe Peano | |
· |
middle dot (for dot product) | 1902 | J. Willard Gibbs |
× |
multiplication sign (for cross product) | ||
∨ |
logical disjunction (a.k.a. OR) | 1906 | Bertrand Russell |
(…) |
matrix notation | 1909[1] | Maxime Bôcher |
[…] |
1909[1] | Gerhard Kowalewski | |
∮ |
contour integral sign | 1917 | Arnold Sommerfeld |
ℤ |
Blackboard bold capital Z (for integer numbers set) | 1930 | Edmund Landau |
ℚ |
Blackboard bold capital Q (for rational numbers set) | 1895 | Giuseppe Peano |
∀ |
universal quantifier (for all) | 1935 | Gerhard Gentzen |
∅ |
empty set sign | 1939 | André Weil / Nicolas Bourbaki[2] |
ℂ |
Blackboard bold capital C (for complex numbers set) | 1939 | Nathan Jacobson |
→ |
arrow (for function notation) | 1936 (to denote images of specific elements) | Øystein Ore |
| 1940 (in the present form of f: X → Y) | Witold Hurewicz | ||
∎ |
end of proof sign (a.k.a. tombstone) | 1950[3] | Paul Halmos |
⌊x⌋ ⌈x⌉ |
greatest integer ≤ x (a.k.a. floor) smallest integer ≥ x (a.k.a. ceiling) |
1962[4] | Kenneth E. Iverson |
See also
Sources
- 1 2 3 "Earliest Uses of Symbols for Matrices and Vectors". jeff560.tripod.com. Retrieved 18 December 2016.
- ↑ Weil, André (1992), The Apprenticeship of a Mathematician, Springer, p. 114, ISBN 9783764326500 .
- ↑ Halmos, Paul (1950). Measure Theory. New York: Van Nostrand. pp. vi.
The symbol ∎ is used throughout the entire book in place of such phrases as "Q.E.D." or "This completes the proof of the theorem" to signal the end of a proof.
- ↑ Kenneth E. Iverson (1962), A Programming Language, Wiley, retrieved 20 April 2016
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