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Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
First and foremost, a word is basically a sequence of symbols, or letters, in a finite set. [1] One of these sets is known by the general public as the alphabet. 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 ...
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
An example of a counting problem whose solution can be given in terms of the Narayana numbers (,), is the number of words containing pairs of parentheses, which are correctly matched (known as Dyck words) and which contain distinct nestings.
The look-and-say sequence is also popularly known as the Morris Number Sequence, after cryptographer Robert Morris, and the puzzle "What is the next number in the sequence 1, 11, 21, 1211, 111221?" is sometimes referred to as the Cuckoo's Egg , from a description of Morris in Clifford Stoll 's book The Cuckoo's Egg .
If s is an infinite sequence word and w is a finite word, let μ N (w) denote the number of occurrences of w as a factor in the prefix of s of length N + |w| − 1. If μ N (w) has a limit as N→∞, we call this the frequency of w, denoted by μ(w). [4]: 73 For a Sturmian word s, every finite factor has a frequency.
Multiplier (linguistics) – Word indicating multiples of an object; Ordinal indicator – Character(s) following an ordinal number (used when writing ordinal numbers, such as a super-script) Ordinal number – Generalization of "n-th" to infinite cases (the related, but more formal and abstract, usage in mathematics) Ordinal data, in statistics
Every infinite sequence of real numbers has an infinite monotone subsequence (This is a lemma used in the proof of the Bolzano–Weierstrass theorem). Every infinite bounded sequence in R n {\displaystyle \mathbb {R} ^{n}} has a convergent subsequence (This is the Bolzano–Weierstrass theorem ).
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