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This definition covers several different uses of the word "sequence", including one-sided infinite sequences, bi-infinite sequences, and finite sequences (see below for definitions of these kinds of sequences). However, many authors use a narrower definition by requiring the domain of a sequence to be the set of natural numbers. This narrower ...
Latin and Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.
As an example, the sequence is frequently in the interval (1/2, 3/2), because there are arbitrarily large n for which the value of the sequence is in the interval. formal, formally Qualifies anything that is sufficiently precise to be translated straightforwardly in a formal system.
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 ...
The dual concept of randomness is compressibility ‒ the more random a sequence is, the less compressible, and vice versa. The predictability approach. This paradigm is due to Claus P. Schnorr and uses a slightly different definition of constructive martingales than martingales used in traditional probability theory. [11]
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.
A word n-gram language model is a purely statistical model of language. It has been superseded by recurrent neural network–based models, which have been superseded by large language models. [1] It is based on an assumption that the probability of the next word in a sequence depends only on a fixed size window of previous words.
Strings, also known as "words" or "sentences", over an alphabet are defined as a sequence of the symbols from the alphabet set. [4] For example, the alphabet of lowercase letters "a" through "z" can be used to form English words like "iceberg" while the alphabet of both upper and lower case letters can also be used to form proper names like ...