Jisho

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Wikipedia definition
1. Up toIn mathematics, the phrase up to is useful for modeling fundamental concepts within a realm of mathematical inquiry, and can be compared with the phrase "all other things being equal" in other disciplines. It indicates that its grammatical object is some equivalence class, to be regarded as a single entity, or disregarded as a single entity. If this object is a class of transformations, it implies the equivalence of objects one of which is the image of the other under such a transformation.
Read “Up to” on English Wikipedia
Read “違いを除いて” on Japanese Wikipedia
Read “Up to” on DBpedia

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