Origins of mathematical notation

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Can you name the first mathematicians to use the given notation?

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NotationOriginatorEarliest known usage
Multiplication symbol (×); plus-minus signClavis Mathematicae, published 1631
Perpendicularity sign (⊥)Cursus mathematicus, 1634
Universal quantifier symbol (∀)Untersuchungen ueber das logische Schliessen, 1935
Square root/radical symbol (√)Die Coss, 1525
Big-O notation for asymptotic boundsAnalytische Zahlentheorie, 1894
Obelus (÷) for division, therefore symbol (∴)Teutsche Algebra, 1659
Equals sign (=)The Whetstone of Witte, 1557
Square 'tombstone' symbol (∎/□) for the end of a proof20th century
Curly d (∂) for partial derivativesMemoire sur la manière de distinguer les maxima des minima dans le Calcul des Variations, 1786
Nabla symbol (∇) for vectorial derivatives, etc.19th century
Elongated 'S' (∫) for integralsAnalyseos tetragonisticae pars secunda, 1675
Prime (') notation for total derivativesThéorie des fonctions analytiques, 1797
Less than and greater than symbolsArtis Analyticae Praxis ad Aequationes Algebraicas Resolvenda, published 1631
NotationOriginatorEarliest known usage
Empty set symbol (∅)Éléments de mathématique, 1939
Stylized Greek letter epsilon (∈) for 'is an element of'Arithmetices prinicipia nova methodo exposita, 1899
Infinity symbol (∞)De sectionibus conicis, 1655
Addition (+) and subtraction (-) signsBehende und hüpsche Rechenung auff allen Kauffmanschafft, 1489
Bra-ket notation (⟨| , |⟩) in physicsA New Notation for Quantum Mechanics, 1939
Curly braces ({, }) for enclosing elements of setsEin Beitrag zur Mannifaltigkeitslehre, 1878
Vertical bars around the entries of a matrix for its determinant Cambridge Mathematical Journal, Vol. II, p. 267-271, 1841
Exclamation mark (!) for factorialÉléments d'arithmétique universelle, 1808
Vertical bars for the absolute value of x (|x|)Zur Theorie der Potenzreihen, 1841
Three horizontal lines (≡) for congruence of integersDisquisitiones arithmeticae, 1801
f(x) for a function f of a variable xCommentarii Academiae Scientiarum Petropolitanae, 1734
Greek letter pi (π) for the constant 3.1415...Synopsis palmariorum mathesios, 1706

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