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Does "up to" defined by Pete L. Clark or Tobias Kildetoft relate to the 2020 English meanings from OED?

If not, why did mathematicians utilize "up to"?

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1 Answers1

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In my experience, the most common meaning of "up to" in mathematical literature is "when you do not distinguish the objects that share some property". For example, the following statement

There are 2 groups of order 4, up to isomorphism.

means that when we do not distinguish isomorphic groups, there are only 2 groups of order 4 ($\Bbb Z_4$ and $\Bbb Z_2\times \Bbb Z_2$).

Vim
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    And the connection with the everyday meaning is fairly clear if we expand the sentence like this: Up to (i.e., until) the point at which we start distinguishing isomorphic groups there are two groups of order $4$. – Brian M. Scott Dec 29 '20 at 04:19
  • @BrianM.Scott well noted. – Vim Dec 29 '20 at 04:41