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An infinite sequence of real numbers (in blue). This sequence is neither increasing, decreasing, convergent, nor Cauchy. It is, however, bounded. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms).
A uniformly recurrent word is a recurrent word in which for any given factor X in the sequence, there is some length n X (often much longer than the length of X) such that X appears in every block of length n X. [1] [6] [7] The terms minimal sequence [8] and almost periodic sequence (Muchnik, Semenov, Ushakov 2003) are also used.
The Fibonacci word is an example of a Sturmian word. The start of the cutting sequence shown here illustrates the start of the word 0100101001.. In mathematics, a Sturmian word (Sturmian sequence or billiard sequence [1]), named after Jacques Charles François Sturm, is a certain kind of infinitely long sequence of characters.
A Fibonacci word is a specific sequence of binary digits (or symbols from any two-letter alphabet). The Fibonacci word is formed by repeated concatenation in the same way that the Fibonacci numbers are formed by repeated addition. It is a paradigmatic example of a Sturmian word and specifically, a morphic word.
Note that it is the limit of the sequence a, f(a), f(f(a)), f(f(f(a))), ... It is clearly a fixed point of the endomorphism f: the unique such sequence beginning with the letter a. [2] [3] In general, a morphic word is the image of a pure morphic word under a coding, that is, a morphism that maps letter to letter. [1]
The post 26 Palindrome Examples: Words and Phrases That Are the Same Backwards and Forwards appeared first on Reader's Digest. Palindrome words are spelled the same backward and forward.
A word sequence is shown to be a phrase/constituent if it exhibits one or more of the behaviors discussed below. The analysis of constituent structure is associated mainly with phrase structure grammars , although dependency grammars also allow sentence structure to be broken down into constituent parts.
For example, the word "encyclopedia" is a sequence of symbols in the English alphabet, a finite set of twenty-six letters. Since a word can be described as a sequence, other basic mathematical descriptions can be applied. The alphabet is a set, so as one would expect, the empty set is a subset. In other words, there exists a unique word of ...