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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.)

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    Yes, it's the terms in the corrections that are up to order x^4, not the corrections or the fulfilling. (your first example) Transfers (a quiet pint) and deletions are often made, but this isn't something I'd choose to use. – Edwin Ashworth Sep 5 '17 at 18:49
  • Your understanding of the meanings is correct, up to one detail: Your meaning for the third example assumes that A is the sort of thing that has only magnitude and phase (like a complex number). In general, when one uses expressions like "X up to Y", there is at least a suggestion that Y is less important than X, so that neglecting Y still leaves a reasonable idea about X. – Andreas Blass Nov 4 '17 at 20:52
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No it does not mean that. It's a slight variant on the standard meaning, but the usage is correct as you write it.

A fulfills the condition B up to corrections of order x^4.

This is an abbreviation of

A fulfills the condition B including corrections of order x^n, for n up to 4.

Likewise

A is fixed up to phase 5.

means that with an implied ordering (phases 1 through 5 etc) phases 'up to' phase 5 (i.e. 1 through 4) are fixed. It implies nothing about phase 5 or higher.

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  • What is the ellipsis then in the phrase "A is known up to a constant"? (which is similar as the last example in the OP, whose meaning you've changed in your answer) – Joce Sep 5 '17 at 20:34
  • Honestly I am a bit confused by your answer. First you say that that is not the meaning (i.e., it is wrong?), but afterwards you say it is correct? Also the sentence with "phase 5" does not make sense to me. A complex number can be described by two real parameters, the magnitude/modulus/absolute_value and the phase/argument/angle. The intended statement is that the first one is fixed, but the second one is undetermined. – wea0 Sep 7 '17 at 1:45
  • The context in the question's examples is mathematics, and this answer does not agree with the usual meaning of "up to" in those examples. – Andreas Blass Nov 4 '17 at 20:47
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This is mathematical language, and the usage of "up to" in the sense of "except" is common in mathematics.

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