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

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