Which is correct here: “arbitrary” or “arbitrarily”?

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

Answer

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.

Attribution
Source : Link , Question Author : Michael , Answer Author : Theta30

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