How did 'up to' evolve to mean 'regardless of', in maths?

Even the OED seems not to have featured it. I couldn't find an explanation on Etymonline.

[Wikipedia:] If X is some property or process, the phrase "up to X" means "disregarding a possible difference in X".

So how did up + to combine to mean thus? This especial mathematical meaning seems to jar with its regular meanings in English (which connote some upper bound).

Footnote: If anyone knows of a better reference than Wikipedia, please advise.

Solution 1:

To my mind, the "mathematical" meaning of up to quite accords with the "general" meaning, and also with your intuition of an upper bound.

For example, the stipulation that "the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) is only defined up to an additive constant" [Wikipedia], it is natural to perceive the constant differences there can be between the antiderivatives as upper bounds on the difference.

Likewise, the term adequality, used by Fermat, can arguably be read (translated) as equality up to an infinitesimal (i.e., difference by at most an infinitesimal), as hinted here.

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