SUBSEQUENCES Meaning and
Definition
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Subsequences are mathematical terms used to describe a specific type of sequence. In mathematics, a sequence is an ordered list of numbers, usually denoted by {a1, a2, a3, ... an}. A subsequence, on the other hand, is a sequence that is derived from the original sequence by selecting some of its terms, but without changing the order. It is important to note that the terms in a subsequence do not have to be consecutive.
Formally, a subsequence of a sequence {a1, a2, a3, ... an} is another sequence {b1, b2, b3, ... bm} such that every term in the subsequence (bi) is derived from the original sequence (aj), where j < j+1. In simpler terms, a subsequence is obtained by removing some terms from the original sequence but maintaining the same order.
Subsequences are frequently encountered in various branches of mathematics, including number theory, calculus, and analysis. They are used to study the properties and behavior of sequences in a more focused and specific manner. Furthermore, subsequences are beneficial for understanding the convergent or divergent behavior of sequences. By analyzing subsequences, mathematicians can often make insightful conclusions about the original sequence as a whole.
Common Misspellings for SUBSEQUENCES
Etymology of SUBSEQUENCES
The word "subsequences" is derived from the combination of two words: "sub-" and "sequences".
- "Sub-" is a prefix that comes from Latin and generally means "under", "below", or "less than". It is added to a word to indicate a lower or smaller level of something. In the case of "subsequences", it suggests the idea of sequences that are contained within or are a part of a larger sequence.
- "Sequences" is the plural form of the word "sequence", which comes from the Latin word "sequens", meaning "following" or "to follow". In mathematics and statistics, a sequence refers to an ordered list of elements, often numbers, that follow a specific pattern or rule.
Combining these two parts, "subsequences" refers to the smaller or partial sequences that can be derived from a larger sequence by removing or changing some elements while preserving the order.
