Two mathematical objects a and b are called "equal up to an equivalence relation R" if a and b are related by R, or, in notation, if aRb holds. Since a is related to b if and only if they have the same equivalence class, it is also the case that a and b are equal up to R if and only if the equivalence classes of a and b with respect to R are equal.
Two mathematical objects a and b are called "equal up to an equivalence relation R" if a and b are related by R, or, in notation, if aRb holds. Since a is related to b if and only if they have the same equivalence class, it is also the case that a and b are equal up to R if and only if the equivalence classes of a and b with respect to R are equal.
Source: Wikipedia "Up to" · CC BY-SA 4.0
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