Peanon.
/peɪˈɑːnəʊ/, /ˈpɪənəʊ/, U.S. /peɪˈɑnoʊ/, /ˈpiənoʊ/ Mathematics.
1. Peano curve n. (also Peano's curve) [described by Peano 1890, in Math. Ann. 36 157] any continuous curve which passes through all points of the unit square in two dimensions, esp. when such a curve is the limit of an infinite series of modifications to a simple curve; (also in extended use) such a space-filling curve in higher dimensions.
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the world > relative properties > number > geometry > curve > [noun] > other
quadratrix1656
section1665
family1705
semiparabola1728
tractrix1728
witcha1760
tractory1820
sinusoid1823
tractatrix1828
indicatrix1841
hodograph1847
tetrazomal1867
space curve1875
horograph1879
hypercycle1889
Peano curve1900
multiple arc1967
unknot1971
fractal1975
analemma1978
1900 Trans. Amer. Math. Soc. 1 73 We give below..a geometric determination of Peano's curve.
1945 Duke Math. Jrnl. 12 569 Does there exist a Peano curve x = F(t), y = G(t) such that the components F(t), G(t) are respectively the real and the imaginary parts of the values taken by a power series on its circle of convergence?
1976 Sci. Amer. Dec. 124/3 Peano curves can be drawn just as easily to fill cubes and hypercubes.
1995 Proc. 1994 Biennial Meeting Philos. Sci. Assoc. 2 232 The Peano curve is not an object of visual representation at all. It was originally defined purely arithmetically by Peano, using tenary numbers and was only given a geometric interpretation by Hilbert.
2. Peano arithmetic n. (also Peano's arithmetic) a system of arithmetic based on a theory of natural numbers defined by the Peano axioms, in which such numbers can be represented using only two symbols (one of which is zero).
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the world > relative properties > number > arithmetic > [noun]
arithmeticc1305
numbera1398
calking1398
arsmetryc1454
arith.1600
ciphering1611
epilogisma1646
logistic1656
tale-craft1674
denumeration1851
sums1877
arithmic1879
Peano arithmetic1903
1903 B. Russell Princ. Math. xxix. 239 (note) The present chapter closely follows Peano's arithmetic.
1974 Amer. Math. Soc. 81 301 That the development of real numbers from Peano arithmetic is not done in this book is not objectionable to me: one must stop somewhere in grinding out ordinary mathematics.
2001 Science (Nexis) 2 Mar. 1702 [Gödel's First Incompleteness Theorem] asserts that in any sufficiently rich, effectively axiomatizable first-order system, say first-order Peano Arithmetic, some first-order assertions will be undecidable, in the sense that they are true in some models of that system and false in others.
3.
a. Peano postulates n. (also Peano's postulates) [proposed by Peano Arithmetices principia, nova methodo exposita (1889)] = Peano axioms n. at sense 3b.
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the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > self-evident or accepted without proof > set of
Peano postulates1905
Peano axioms1913
1902 Bull. Amer. Math. Soc. 9 43 Let a and b be..any two elements of a system..which satisfies Peano's five postulates.]
1905 Ann. Math. 6 171 The following sections..are due essentially to Peano (1889), although Peano's postulates for a progression are based not on the notion of order, but on the notion of ‘successor of’.
1944 Ann. Math. Stud. 13 117 The consistency of the system obtained from the foregoing by adding also the axiom of infinity (or Peano's postulates in the form given in 5.3 below) is a much more difficult question.
1982 W. S. Hatcher Logical Found. Math. iii. 88 Mere quantification theory plus the Peano postulates does not suffice for the construction of analysis.
b. Peano axioms n. (also Peano's axioms) a set of axioms (spec. a set of five principal axioms) from which the properties of the natural numbers may be deduced.
ΘΚΠ
the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > self-evident or accepted without proof > set of
Peano postulates1905
Peano axioms1913
1913 Amer. Jrnl. Math. 35 37 This geometry may also be defined by Pasch's axioms..or Peano's axioms I-XVI in his ‘I principii di Geometria’.
1955 W. W. Hall & G. L. Spencer Elem. Topol. iv. 140 The natural numbers or positive integers are given by the so-called Peano axioms.
1979 Sci. Amer. Feb. 5/1 Yuri Matyasevich showed that there is a Diophantine equation that has no solutions in whole numbers but is such that this fact cannot be proved from the Peano axioms.
1992 Mind 101 108 Let PA2 be the conjunction of the second-order Peano axioms.
This entry has been updated (OED Third Edition, September 2005; most recently modified version published online March 2022).
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n.1900