Can "up to" mean neglecting, ignoring, excluding...?

Question

In scientific writing my professor (not a native English speaker) sometimes uses "up to *SOMETHING*" with the intention of expressing that *SOMETHING* is neglected, ignored, or excluded (see the examples below). Is such usage ever correct? (It seems a bit contrary to the widespread use cases such as in "up to five" or "to be up to something".) Is there some other short expression that can be used to convey this intended meaning in general. Here are the examples (First line: what is written. Second line: what is meant.) >A fulfills the condition B up to corrections of order x^4. > >(A fulfills the condition B if we expand everything in x and neglect all terms of x^4 and higher.) or >A equals B up to C-effects. > >(A equals B if the effects of the phenomenon C are ignored.) or >A is fixed up to a phase. > >(We can determine the magnitude of A, but not the phase.)

Answer 1

It sounds to me like he may just have the idiom slightly wrong? When I read the examples you provided, I think “up to the point where’” (or “when” or “of,” depending on the sentence) would work, as in “A fulfills the condition B up to the point where corrections of...”; or “A equals B up to the point when C-effects are encountered.” He could also just be confusing “up to” with “until,” which seems like it could be substituted in his sentences to better convey the intended meaning than “up to” by itself does. Either way, it’s still not the most elegant way of expressing what he means, but it may explain how he came to adopt the phrasing he uses.