منابع مشابه
There are less transcendental numbers than rational numbers
According to a basic theorem of transfinite set theory the set of irrational numbers is uncountable, while the set of rational numbers is countable. This is contradicted by the fact that any pair of irrational numbers is separated by at least one rational number. Hence, in the interval [0,1] there exist more rational numbers than irrational numbers.
متن کاملCongruent numbers with many prime factors.
Mohammed Ben Alhocain, in an Arab manuscript of the 10th century, stated that the principal object of the theory of rational right triangles is to find a square that when increased or diminished by a certain number, m becomes a square [Dickson LE (1971) History of the Theory of Numbers (Chelsea, New York), Vol 2, Chap 16]. In modern language, this object is to find a rational point of infinite ...
متن کاملSome Families of Non-congruent Numbers
In this article we study the Tate-Shafarevich groups corresponding to 2-isogenies of the curve Ek : y 2 = x(x2 − k2) and construct infinitely many examples where these groups have odd 2-rank. Our main result is that among the curves Ek, where k = pl ≡ 1 mod 8 for primes p and l, the curves with rank 0 have density ≥ 1 2 .
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We compare the complexities of the following two model checking problems: checking whether a linear-time formula is satis ed by all paths (which we call universal model checking) and checking whether a formula is satis ed by almost all paths (which we call fair model checking here). For many interesting classes of linear-time formulas, both problems have the same complexity: for instance, they ...
متن کاملExtend a ranking method of trapezoidal fuzzy numbers to all fuzzy numbers by a weighting functions
Recently Abbasbandy and Hajjari (Computers and Mathematics with Applications57 (2009) 413-419) have introduced a ranking method for the trapezoidalfuzzy numbers. This paper extends theirs method to all fuzzy numbers,which uses from a defuzzication of fuzzy numbers and a general weightingfunction. Extended method is interesting for ranking all fuzzy numbers, and itcan be applied for solving and ...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1998
ISSN: 0386-2194
DOI: 10.3792/pjaa.74.29