Up to

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

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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.

Related Topics:
Mathematics - Equivalence class - Group theory - Group - Acting

~ ~ ~ ~ ~ ~ ~ ~ ~ ~