Editing Up to (section)

===Group theory===
In [[group theory]], one may have a [[group (mathematics)|group]] {{mvar|G}} [[Group action (mathematics)|acting]] on a set {{mvar|X}}, in which case, one might say that two elements of {{mvar|X}} are equivalent "up to the group action"—if they lie in the same [[Group action (mathematics)|orbit]].

Another typical example is the statement that "there are two different [[group (mathematics)|groups]] of order 4 up to [[isomorphism]]", or "modulo isomorphism, there are two groups of order 4". This means that, if one considers [[group isomorphism|isomorphic]] groups "equivalent", there are only two equivalence classes of groups of order 4.