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The Collaborative International Dictionary
At any rate

Any \A"ny\, a. & pron. [OE. [ae]ni[yogh], [ae]ni, eni, ani, oni, AS. [=ae]nig, fr. [=a]n one. It is akin to OS. [=e]nig, OHG. einic, G. einig, D. eenig. See One.]

  1. One indifferently, out of an indefinite number; one indefinitely, whosoever or whatsoever it may be.

    Note: Any is often used in denying or asserting without limitation; as, this thing ought not be done at any time; I ask any one to answer my question.

    No man knoweth the Son, but the Father; neither knoweth any man the Father, save the Son.
    --Matt. xi. 27.

  2. Some, of whatever kind, quantity, or number; as, are there any witnesses present? are there any other houses like it? ``Who will show us any good?''
    --Ps. iv. 6.

    Note: It is often used, either in the singular or the plural, as a pronoun, the person or thing being understood; anybody; anyone; (pl.) any persons.

    If any of you lack wisdom, let him ask of God, . . . and it shall be given him.
    --Jas. i. 5.

    That if he found any of this way, whether they were men or women, he might bring them bound unto Jerusalem.
    --Acts ix. 2.

    At any rate, In any case, whatever may be the state of affairs; anyhow.

Wiktionary
at any rate

prep.phr. (lb en conjunctive) in any case, anyway, anyhow, regardless; ''used to discard a previous thought''.

WordNet
at any rate
  1. adv. used to indicate that a statement explains or supports a previous statement; "Anyhow, he is dead now"; "I think they're asleep; anyhow, they're quiet"; "I don't know what happened to it; anyway, it's gone"; "anyway, there is another factor to consider"; "I don't know how it started; in any case, there was a brief scuffle"; "in any event, the government faced a serious protest"; "but at any rate he got a knighthood for it" [syn: anyhow, anyway, in any case, in any event]

  2. if nothing else (`leastwise' is informal and `leastways' is colloquial); "at least he survived"; "they felt--at any rate Jim felt--relieved though still wary"; "the influence of economists--or at any rate of economics--is far-reaching" [syn: at least, leastways, leastwise]

Usage examples of "at any rate".

He hadn't argued when she finally went to him to demand something to help her sleep, at any rate.