subsequence etymology

Etymology and Meaning

The word "subsequence" is derived from two Latin words:

• "sub-" (under, below)
• "sequentia" (a following)

Hence, a subsequence is a sequence that appears within a larger sequence, but not necessarily in the same order.

Origin

The concept of a subsequence can be traced back to the work of mathematicians in the 19th century. In 1877, the Italian mathematician Giuseppe Peano defined a subsequence as follows:

If A is a sequence, then a subsequence B is a sequence such that for every natural number n, there exists a natural number m such that Bn = Am for all n ≥ m.

This definition, which is still used today, captures the idea that a subsequence is a sequence that can be "extracted" from a larger sequence by skipping over some elements.

Example

Consider the sequence A = (1, 2, 3, 4, 5, 6, 7, 8).

The sequence B = (1, 3, 5, 7) is a subsequence of A, because we can obtain B from A by skipping over the elements 2, 4, 6, and 8.

Applications

The concept of a subsequence has important applications in mathematics, computer science, and other fields. For example:

• In combinatorics, subsequences are used to count the number of ways to select a subset of elements from a set.
• In algorithm design, subsequences are used to find the longest common subsequence of two sequences, which is a useful technique in data compression and pattern matching.
• In analysis, subsequences are used to study the convergence of sequences and to prove the existence of limits.

subsequence relate terms

• subsequent

  Etymology Latin subsequens meaning following or coming after From the prefix s

• sequel

  Etymology The word sequel comes from the Latin word sequēla which means a following

• termination

  Etymology The word termination comes from the Latin word terminatio which means en

• result

  Etymology The word result comes from the Middle English word resulte which in turn

• luster

  Etymology Middle English lustre from Old French lustre from Latin lūstrum wash pu

• rustle

  Etymology The word rustle is believed to have originated from two possible sources O

• sutler

  Etymology The word sutler comes from the Middle English word sotelar which in turn

• priority

  Etymology The word priority comes from the Latin word prioritas which means the st

• outcome

  Etymology From Middle English out come from Old English ūt cuman from ūt out

• tribe

  Etymology The word tribe comes from the Latin word tribus which referred to one of

• journey

  Etymology and Meaning The word journey originates from the Old French word journee