| 释义 |
Peano, n. Math.|peɪˈɑːnəʊ|
The name of Giuseppe Peano (1858–1932), Italian mathematician, used attrib. and in the possessive to designate concepts introduced by him or arising out of his work, as Peano('s) axioms n. pl., a set of axioms proposed by him (1891, in Rivista di Matematica I. 91) from which may be deduced the properties of the natural numbers; Peano curve, any continuous curve, such as the one described by Peano (1890, in Math. Ann. XXXVI. 157), 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 used analogously of such a space-filling curve in higher dimensions; Peano('s) postulates n. pl. = Peano('s) axioms above.
[1897Bulletin des Sciences Mathématiques XXI. 263 Ainsi la courbe de M. Peano est continue.] 1900Trans. Amer. Math. Soc. I. 73 We give below..a geometric determination of Peano's curve... The analytic formulas for the Peano functions given by Cesàro. 1903B. Russell Princ. Math. I. xiv. 125 Peano's primitive propositions are then the following. (1) 0 is a number. (2) If a is a number, the successor of a is a number [etc.]. 1919― Introd. Math. Philos. i. 7 Let ‘0’ mean the number one, let ‘number’ mean the set 1, 1 / 2, 14, 18, 116 ,...and let ‘successor’ mean ‘half’. Then all Peano's five axioms will be true of this set. 1944Annals Math. Stud. XIII. 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. 1945Duke Math. Jrnl. XII. 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? 1955Hall & Spencer Elem. Topol. iv. 140 The natural numbers or positive integers are given by the so-called Peano axioms. 1976Sci. Amer. Dec. 124/3 Peano curves can be drawn just as easily to fill cubes and hypercubes. 1979Ibid. 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. 1982W. S. Hatcher Logical Found. Math. iii. 88 Mere quantification theory plus the Peano postulates does not suffice for the construction of analysis. |