Up to

:This article is about the sense of "up to" used in mathematics. See for other definitions.

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In mathematics, the phrase "up to xxxx" indicates that members of an equivalence class are to be regarded as a single entity for some purpose. "xxxx" describes a property or process which transforms an element into one from the same equivalence class, i.e. one which is considered equivalent to it. In group theory, for example, we may have a group G acting on a set X, in which case we say that two elements of X are equivalent "up to the group action" if they lie in the same orbit.

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Equivalence class: In mathematics, given a set X and an equivalence relation ~ on X, the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a:...

Group theory: Group theory is that branch of mathematics concerned with the study of groups....

Group: The term group can refer to several concepts:...

Up to related Images and Photos (experimental)

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