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- Up_to abstract "In mathematics, the phrase up to appears in discussions about the elements of a set (say S), and the conditions under which subsets of those elements may be considered equivalent. The statement \"elements a and b of set S are equivalent up to X\" means that a and b are equivalent if criterion X (such as rotation or permutation) is ignored. That is, a and b can be transformed into one another if a transform corresponding to X (rotation, permutation etc.) is applied.Looking at the entire set S, when X is ignored the elements can be arranged in subsets whose elements are equivalent (\"equivalent up to X\"). Such subsets are called \"equivalence classes\". If X is some property or process, the phrase \"up to X\" means \"disregarding a possible difference in X\". For instance the statement \"an integer's prime factorization is unique up to ordering\", means that the prime factorization is unique if we disregard the order of the factors. We might say \"the solution to an indefinite integral is f(x), up to addition by a constant\", meaning that the added constant is not the focus here, the solution f(x) is, and that the addition of a constant is to be regarded as a background, of secondary focus. Further examples concerning up to isomorphism, up to permutations and up to rotations are described below.In informal contexts, mathematicians often use the word modulo (or simply \"mod\") for similar purposes, as in \"modulo isomorphism\".".
- Up_to thumbnail Partitions_of_6-set_with_3_singletons.svg?width=300.
- Up_to wikiPageExternalLink upto.
- Up_to wikiPageID "44787".
- Up_to wikiPageLength "5763".
- Up_to wikiPageOutDegree "39".
- Up_to wikiPageRevisionID "707308529".
- Up_to wikiPageWikiLink Abuse_of_notation.
- Up_to wikiPageWikiLink Adequality.
- Up_to wikiPageWikiLink Antiderivative.
- Up_to wikiPageWikiLink Bisimulation.
- Up_to wikiPageWikiLink Category:Mathematical_terminology.
- Up_to wikiPageWikiLink Ceteris_paribus.
- Up_to wikiPageWikiLink Chessboard.
- Up_to wikiPageWikiLink Constant_of_integration.
- Up_to wikiPageWikiLink Eight_queens_puzzle.
- Up_to wikiPageWikiLink Equivalence_class.
- Up_to wikiPageWikiLink Group_(mathematics).
- Up_to wikiPageWikiLink Group_action.
- Up_to wikiPageWikiLink Group_isomorphism.
- Up_to wikiPageWikiLink Group_theory.
- Up_to wikiPageWikiLink Hyperreal_number.
- Up_to wikiPageWikiLink Infinitesimal.
- Up_to wikiPageWikiLink Isomorphism.
- Up_to wikiPageWikiLink Mathematical_proof.
- Up_to wikiPageWikiLink Mathematics.
- Up_to wikiPageWikiLink Modulo_(jargon).
- Up_to wikiPageWikiLink Permutation.
- Up_to wikiPageWikiLink Quotient_group.
- Up_to wikiPageWikiLink Reflection_(mathematics).
- Up_to wikiPageWikiLink Rotation.
- Up_to wikiPageWikiLink Rotation_(mathematics).
- Up_to wikiPageWikiLink Standard_part_function.
- Up_to wikiPageWikiLink Symmetry.
- Up_to wikiPageWikiLink Synecdoche.
- Up_to wikiPageWikiLink Tetris.
- Up_to wikiPageWikiLink Tetromino.
- Up_to wikiPageWikiLink File:Partitions_of_6-set_with_3_singletons.svg.
- Up_to wikiPageWikiLink File:Skak_8dronning.png.
- Up_to wikiPageWikiLink File:Tetrominoes_IJLO_STZ_Worlds.svg.
- Up_to wikiPageWikiLinkText "Up to".
- Up_to wikiPageWikiLinkText "counted as one".
- Up_to wikiPageWikiLinkText "up to isomorphism".
- Up_to wikiPageWikiLinkText "up to".
- Up_to wikiPageUsesTemplate Template:Math.
- Up_to wikiPageUsesTemplate Template:Wiktionary.
- Up_to subject Category:Mathematical_terminology.
- Up_to comment "In mathematics, the phrase up to appears in discussions about the elements of a set (say S), and the conditions under which subsets of those elements may be considered equivalent. The statement \"elements a and b of set S are equivalent up to X\" means that a and b are equivalent if criterion X (such as rotation or permutation) is ignored.".
- Up_to label "Up to".
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- Up_to sameAs Llevat_de.
- Up_to sameAs Až_na.
- Up_to sameAs Salvo_(matemáticas).
- Up_to sameAs À_quelque_chose_près.
- Up_to sameAs עד_כדי_(מתמטיקה).
- Up_to sameAs 違いを除いて.
- Up_to sameAs Salvo_(matemática).
- Up_to sameAs m.0c67m.
- Up_to sameAs Q2914964.
- Up_to sameAs Up_to.
- Up_to wasDerivedFrom Up_to?oldid=707308529.
- Up_to depiction Partitions_of_6-set_with_3_singletons.svg.
- Up_to isPrimaryTopicOf Up_to.