In 1929 Otto Haupt used G 0 for the integers and Ρ 0 (capital rho ) for the rationals in Einführung in die Algebra I and II, Leipzig 1929. Hasse's choice of gamma and rho may have been determined by the initial letters of the German terms "ganze Zahl" (integer ) and "rationale Zahl" (rational ). He kept to this notation in his later books on number theory. In 1926 Helmut Hasse (1898- 1979) used Γ for the integers and Ρ (capital rho ) for the rationals in Höhere Algebra I and II, Berlin 1926. ![]() In 1895 in his Formulaire de mathématiques, Peano used N for the positive integers, n for integers, N 0 for the positive integers and zero, R for positive rational numbers, r for rational numbers, Q for positive real numbers, q for real numbers, and Q 0 for positive real numbers and zero. Peano used N, R, and Q and showed their meaning in a table on page 23: ![]() In 1889 Giuseppe Peano cited Dedekind's book in his Arithmetices prinicipia nova methodo exposita, and used the same symbol for the positive integers as Dedekind. In 1888 Richard Dedekind denoted the natural numbers by N in Was ist und was sollen die Zahlen, § 6. Dedekind also used K for the integers and J for complex numbers. In 1872 Richard Dedekind denoted the rationals by R and the reals by blackletter R in Stetigkeit und irrationale Zahlen (1872) ( Continuity and irrational numbers Works, 3, 315- 334. The authors of classical textbooks such as Weber and Fricke did not denote particular domains of computation with letters. Letters for the sets of rational and real numbers. Edmund Landau used π ( x ) for the number of primes less than or equal to x in 1909 in Handbuch der Lehre von der Verteilung der Primzahlen ( Cajori vol. However, Gauss had used the symbol much earlier in his personal writings (Francis, page 82). The citation above is from Disquisitiones arithmeticae (Leipzig, 1801), art. Numerorum congruentiam hoc signo, ≡, in posterum denotabimus, modulum ubi opus erit in clausulis adiungentes, - 16 ≡ 9 (mod. The congruent symbol used in number theory ≡ was introduced in print in 1801 by Carl Friedrich Gauss (1777- 1855) in Disquisitiones arithmeticae: ![]() In 1927 Edmund Landau used a| b in Elementary Number Theory. In the unpublished notes of his 1925 number theory seminar, Hardy used a| b several times in reference to work by Polya.
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