AskDefine | Define nearly

Dictionary Definition

nearly adv
1 (of actions or states) slightly short of or not quite accomplished; `near' is sometimes used informally for `nearly' and `most' is sometimes used informally for `almost'; "the job is (just) about done"; "the baby was almost asleep when the alarm sounded"; "we're almost finished"; "the car all but ran her down"; "he nearly fainted"; "talked for nigh onto 2 hours"; "the recording is well-nigh perfect"; "virtually all the parties signed the contract"; "I was near exhausted by the run"; "most everyone agrees" [syn: about, just about, almost, most, all but, near, nigh, virtually, well-nigh]
2 in a close manner; "the two phenomena are intimately connected"; "the person most nearly concerned" [syn: closely, intimately]

User Contributed Dictionary

English

Pronunciation

Adverb

  1. almost, but not quite; slightly short of
  2. intimately

Translations

almost, but not quite

Extensive Definition

In mathematics, especially in set theory, when dealing with sets of infinite size, the term almost or nearly is used to mean all the elements except for finitely many.
In other words, an infinite set S that is a subset of another infinite set L, is almost L if the subtracted set L\S is of finite size.
Examples:
  • The set S = \ is almost N for any k in N, because only finitely many natural numbers are less than k.
  • The set of prime numbers is not almost N because there are infinitely many natural numbers that are not prime numbers.
This is conceptually similar to the almost everywhere concept of measure theory, but is not the same. For example, the Cantor set is uncountably infinite, but has Lebesgue measure zero. So a real number in (0, 1) is a member of the complement of the Cantor set almost everywhere, but it is not true that the complement of the Cantor set is almost the real numbers in (0, 1).
nearly in German: Fast alle
nearly in Esperanto: Vikipedio:Projekto matematiko/Preskaŭ
nearly in Hungarian: Majdnem
nearly in Chinese: 幾乎

Synonyms, Antonyms and Related Words

about, all but, all in all, almost, almost entirely, approaching, approximately, around, as good as, barely, by and large, chiefly, circa, close, close to, closely, effectually, essentially, exactly, hardly, identically, in, in effect, in essence, in the main, just about, mainly, more or less, most, mostly, much, narrowly, near, nearabout, nearing, nigh, nighhand, not quite, on balance, on the whole, only just, plus ou moins, practically, precisely, pretty near, roughly, round, roundly, rudely, say, scarcely, some, somewhere, substantially, virtually, well-nigh
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