# Definition talk:Sufficiently Small

Regarding the ambiguity referred to in the "also known as" section, what should the $\mathsf{Pr} \infty \mathsf{fWiki}$ convention be regarding using the phrase "sufficiently small" to refer to a negative $\epsilon < 0$ sufficiently small? My vote: use phrases along the lines of "$\epsilon$ for $|\epsilon|$ sufficiently small". This avoids the ambiguity but also feels less awkward than "sufficiently small in absolute value". The same convention could be used for $M \ll 0$ and "$|M|$ sufficiently large". GFauxPas (talk)
"Sufficiently small in magnitude" is adequate if you really want to pin it down. But if you have already specified the $+$ness of $\epsilon$ there's no need to specify its "absolute value" for apparent reasons. If you do ever need to use "sufficiently small" to mean "sufficiently negative", then IMO "sufficiently large (in magnitude)" coupled with a statement to the effect that the quantity in question is specifically less than zero would do the trick. But I don't think I've ever encountered the situation where this has ever been needed.
If you really want to be precise, and $\epsilon$ genuinely might be a positive or negative small value, you can always say "for sufficiently small $|\epsilon|$" and the job is done. --prime mover (talk) 10:42, 28 May 2018 (EDT)