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- Up_to abstract "In mathematics, the phrase up to 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 (such as "isomorphism" or "permutation"), it implies the equivalence of objects one of which is the image of the other under such a transformation.If X is some property or process, the phrase "up to X" means "disregarding a possible difference in X". For instance we might follow the statement "an integer's prime factorization is unique up to ordering", meaning that the prime factorization is unique if we disregard the order of the factors; or 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 "5298".
- Up_to wikiPageOutDegree "40".
- Up_to wikiPageRevisionID "678259833".
- Up_to wikiPageWikiLink Abuse_of_notation.
- Up_to wikiPageWikiLink Adequality.
- Up_to wikiPageWikiLink All_other_things_being_equal.
- 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 Image_(mathematics).
- Up_to wikiPageWikiLink Indefinite_integral.
- 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 Proof_techniques.
- Up_to wikiPageWikiLink Quotient_group.
- Up_to wikiPageWikiLink Quotient_set.
- Up_to wikiPageWikiLink Reflection_(mathematics).
- Up_to wikiPageWikiLink Rotation.
- 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 hasPhotoCollection 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 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 (such as "isomorphism" or "permutation"), it implies the equivalence of objects one of which is the image of the other under such a transformation.If X is some property or process, the phrase "up to X" means "disregarding a possible difference in X".".
- Up_to label "Up to".
- 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 Q2914964.
- Up_to sameAs Up_to.
- Up_to wasDerivedFrom Up_to?oldid=678259833.
- Up_to depiction Partitions_of_6-set_with_3_singletons.svg.
- Up_to isPrimaryTopicOf Up_to.