Repetitions in Words Associated with Parry Numbers
... Let w be a factor of an infinite binary word u such that ∞ > ind(w) > 1 and let w have the maximal index among its conjugates. Put k := bind(w)c and denote w 0 the prefix of w such that w ind(w) = w k w 0 . Then (i) all the following factors are bispecial: w 0 , ww 0 , . . . , w k −1 w 0 , (ii) ther ...
... Let w be a factor of an infinite binary word u such that ∞ > ind(w) > 1 and let w have the maximal index among its conjugates. Put k := bind(w)c and denote w 0 the prefix of w such that w ind(w) = w k w 0 . Then (i) all the following factors are bispecial: w 0 , ww 0 , . . . , w k −1 w 0 , (ii) ther ...
Double sequences of interval numbers defined by Orlicz functions
... Chiao [1] introduced sequences of interval numbers and defined the usual convergence of sequences of interval numbers. Şengönül and Eryılmaz [18] introduced and studied bounded and convergent sequence spaces of interval numbers and showed that these spaces are complete metric spaces. Recently, Es ...
... Chiao [1] introduced sequences of interval numbers and defined the usual convergence of sequences of interval numbers. Şengönül and Eryılmaz [18] introduced and studied bounded and convergent sequence spaces of interval numbers and showed that these spaces are complete metric spaces. Recently, Es ...
Exercises 09
... the 110 hours of practice can be distributed among them. And since 110 > 18 × 6 = 108, the generalized pigeonhole principle implies that some consecutive 2 −day period contains at least 19 hours. 11) Split the triangle into four smaller ones by connecting midpoints of its sides. The largest possible ...
... the 110 hours of practice can be distributed among them. And since 110 > 18 × 6 = 108, the generalized pigeonhole principle implies that some consecutive 2 −day period contains at least 19 hours. 11) Split the triangle into four smaller ones by connecting midpoints of its sides. The largest possible ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.