Bien means well or good. But I have seen in some cases these two meanings do not fit well. For example, in "Étant donnée une F, ou bien elle est formée d'une relation de base finie, ou bien...", "ou bien" translated to "or well" does not sound good.

So I wonder what is the exact meaning of bien above.

  • Bien has no independent meaning in the ou bien set phrase. On the other hand, bien has its own meaning in the now deleted ...atteint bien A example, but that's a different question. – jlliagre May 15 at 23:40

Ou bien” is a set phrase which is practically synonymous with “ou” or “soit”: the whole phrase “ou bien” means “or” (or “either” when it's in lead position). It is usually constructed like “soit”, i.e. it is present before the first alternative as well as between alternatives. The following are roughly equivalent and mean “[either] A or B”:

A ou B
A ou alors B   (usually used when A and B are very long phrases)
A ou bien B
ou bien A, ou bien B
soit A soit B

There is a nuance in that “soit” is more likely to be an exclusive or, and “ou bien” a little more likely to be exclusive than “ou”. However, all the formulations can either be exclusive or inclusive. In math, “ou” is always exclusive, but in everyday language, it's often exclusive and “et/ou” can be used (mostly in writing) to indicate an inclusive or (and like “and/or” in English, not everyone likes it). “Ou bien” and “soit” are ambiguous even in math: they're usually exclusive but can be inclusive.

  • “Ou alors” seems also exclusive to me, especially in math – James Silipo May 15 at 20:08
  • @JamesSilipo Like “ou”, it often is, but not always. Unlike “ou”, it can be exclusive in math. – Gilles 'SO nous est hostile' May 15 at 20:17
  • “Ou alors” souds to me like “ou autrement” e.g. “Un anneau est intègre ou alors il ne l’est pas” – James Silipo May 15 at 20:21
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    @hermes "Le nombre des y distincts atteint bien A." → “bien” means “indeed”. The meaning is unrelated. But please don't add unrelated questions to your existing questions. – Gilles 'SO nous est hostile' May 15 at 21:36
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    @Jonathan sorry but in your second example, if he comes by plane, this excludes that he comes by car or train! Isn’t it? – James Silipo May 16 at 19:21

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