About: Abuse of notation

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In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not entirely formally correct, but which might help simplify the exposition or suggest the correct intuition (while possibly minimizing errors and confusion at the same time). However, since the concept of formal/syntactical correctness depends on both time and context, certain notations in mathematics that are flagged as abuse in one context could be formally correct in one or more other contexts. Time-dependent abuses of notation may occur when novel notations are introduced to a theory some time before the theory is first formalized; these may be formally corrected by solidifying and/or otherwise improving the theory. Abuse of notation should be contrasted with misuse of notation, which

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rdfs:label	Abuse of notation (en)
rdfs:comment	In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not entirely formally correct, but which might help simplify the exposition or suggest the correct intuition (while possibly minimizing errors and confusion at the same time). However, since the concept of formal/syntactical correctness depends on both time and context, certain notations in mathematics that are flagged as abuse in one context could be formally correct in one or more other contexts. Time-dependent abuses of notation may occur when novel notations are introduced to a theory some time before the theory is first formalized; these may be formally corrected by solidifying and/or otherwise improving the theory. Abuse of notation should be contrasted with misuse of notation, which (en)
sameAs	Abuse of notation
dbp:wikiPageUsesTemplate	dbt:Anchor dbt:Math dbt:More_citations_needed dbt:Mvar dbt:Reflist dbt:Short_description
Subject	Mathematical notation Mathematical terminology
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Abuse_of_notation?oldid=1065592820&ns=0
Wikipage page ID	1698066 (xsd:integer)
page length (characters) of wiki page	8939 (xsd:nonNegativeInteger)
Wikipage revision ID	1065592820 (xsd:integer)
Link from a Wikipage to another Wikipage	Group (mathematics) Logical intuition Addition Almost everywhere Universal property Three-dimensional graph Cartesian product Category (mathematics) Category theory General linear group Mathematical notation Mathematical terminology Set (mathematics) Constant function Morphism Open set Operation (mathematics) Order (group theory) Partial function Partition of a set Equivalence class Equivalence relation Finite group Misnomer Group homomorphism Group representation Group theory Integer Modular arithmetic Vector space Euclidean space Subset Topological space Isomorphism Lebesgue integration Mathematical notation Mathematical object Mathematics Measure space The Times (disambiguation) Natural transformation Ring (mathematics)
has abstract	In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not entirely formally correct, but which might help simplify the exposition or suggest the correct intuition (while possibly minimizing errors and confusion at the same time). However, since the concept of formal/syntactical correctness depends on both time and context, certain notations in mathematics that are flagged as abuse in one context could be formally correct in one or more other contexts. Time-dependent abuses of notation may occur when novel notations are introduced to a theory some time before the theory is first formalized; these may be formally corrected by solidifying and/or otherwise improving the theory. Abuse of notation should be contrasted with misuse of notation, which does not have the presentational benefits of the former and should be avoided (such as the misuse of constants of integration). A related concept is abuse of language or abuse of terminology, where a term — rather than a notation — is misused. Abuse of language is an almost synonymous expression for abuses that are non-notational by nature. For example, while the word representation properly designates a group homomorphism from a group G to GL(V), where V is a vector space, it is common to call V "a representation of G". Another common abuse of language consists in identifying two mathematical objects that are different, but canonically isomorphic. Other examples include identifying a constant function with its value, identifying a group with a binary operation with the name of its underlying set, or identifying to the Euclidean space of dimension three equipped with a Cartesian coordinate system. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Abuse_of_notation
is Wikipage redirect of	Abuse of terminology Abuse of Notation
is Link from a Wikipage to another Wikipage of	Group (mathematics) Norm (mathematics) Number Abuse of language Abuse of terminology Adjoint functors Affine symmetric group Algebraic structure Anyon Asymptotic analysis Big O notation Bochner space Branch point Bra–ket notation Generalized permutation matrix Germ (mathematics) Dirac delta function Dirac equation Direct limit Disjoint union Distribution (mathematics) Divergence History of mathematical notation Jet (mathematics) Musical isomorphism Classification of discontinuities Cylinder set measure List of set identities and relations Compressed sensing Constructive set theory Holomorphic vector bundle Homotopy groups of spheres Minkowski space Notation Equivalent definitions of mathematical structures Fisher information metric Function (mathematics) Gamma matrices Ideal norm

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