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This narrower definition has the disadvantage that it rules out finite sequences and bi-infinite sequences, both of which are usually called sequences in standard mathematical practice. Another disadvantage is that, if one removes the first terms of a sequence, one needs reindexing the remainder terms for fitting this definition.
Punctuation can be used to introduce ambiguity or misunderstandings where none needed to exist. One well known example, [17] for comedic effect, is from A Midsummer Night's Dream by William Shakespeare (ignoring the punctuation provides the alternate reading).
In linguistics and grammar, a sentence is a linguistic expression, such as the English example "The quick brown fox jumps over the lazy dog."In traditional grammar, it is typically defined as a string of words that expresses a complete thought, or as a unit consisting of a subject and predicate.
Whether a listener is present or not is sometimes irrelevant. It answers the question: "Why has this been said?" The five basic sentence forms (or "structures") in English are the declarative, interrogative, exclamative, imperative and the optative. These correspond to the discourse functions statement, question, exclamation, and command ...
In Latin, the sequence of tenses rule affects dependent verbs in the subjunctive mood, mainly in indirect questions, indirect commands, and purpose clauses. [4] If the main verb is in one of the non-past tenses, the subordinate verb is usually in the present or perfect subjunctive (primary sequence); if the main verb is in one of the past tenses, the subordinate verb is usually in the ...
The central question to be posed is the nature of the intersection over all the natural numbers, or, put differently, the set of numbers, that are found in every Interval (thus, for all ). In modern mathematics, nested intervals are used as a construction method for the real numbers (in order to complete the field of rational numbers).
Since the topological vector space definition of Cauchy sequence requires only that there be a continuous "subtraction" operation, it can just as well be stated in the context of a topological group: A sequence () in a topological group is a Cauchy sequence if for every open neighbourhood of the identity in there exists some number such that ...
For example, the sequence ,, is a subsequence of ,,,,, obtained after removal of elements ,, and . The relation of one sequence being the subsequence of another is a partial order . Subsequences can contain consecutive elements which were not consecutive in the original sequence.