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Do you say "an arbitrarily small constant epsilon" or "an arbitrary small constant epsilon"? Or are both correct?

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I would say "an arbitrarily small constant epsilon" because arbitrarily is an adverb that modifies the adjective small. This is the usual meaning of the constant epsilon—that it can become as small as possible.

However, "an arbitrary small constant epsilon" has meaning in itself in the sense of a constant that is small and arbitrary. The word small would be then relative.

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  • This is what I couldn't figure out... Good answer, +1.
    – Alenanno
    Apr 30, 2011 at 7:59
  • 'Arbitrarily' is an adverb modifying an adjective, 'arbitrary' is an adjective.
    – neontapir
    Jan 4, 2014 at 0:21
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    After you introduce "an arbitrarily small constant epsilon" you may later remind the reader of its property by talking about "the arbitrary smallness of epsilon"... since now "arbitrary" is an adjective.
    – GEdgar
    Jan 4, 2014 at 15:15

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