Does "may not" mean that never allowed or sometimes not allowed? For example: the sequence may not converge. Does this mean that the sequence never converges or that there is no guarantee that the sequence converges?
2026-05-04 15:48:11.1777909691
Mathematical meaning of "may not"
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In everyday English, the construction "$X$ may not $Y$" can mean either that it is not allowed for $X$ to do $Y$, or that it is possible/conceivable that $X$ does not do $Y$. One needs to look to context and semantics to find out which of these in the case.
In mathematics it is unusual to speak about permission at all -- mathematical objects do whatever they do whether we want them to or not -- so generally the only meaning that makes sense in a mathematical context is that it is possible that $X$ does not do $Y$.