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too simple to be simple in nLab

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Quite often, classical references will define ‘simple’ (or an analogous term) in naïve way, so that a ‘trivial’ object is simple, but later it will become clear that more sophisticated theorems (especially classification theorems) work better if the definition is changed so that the trivial object is not simple. Usually this can be done by changing ‘if’ to ‘iff’ (or sometimes changing ‘or’ to ‘xor’) in the classical definition.

too simple to be simple in nLab nLab too simple to be simple Skip the Navigation Links | Home Page | All Pages | Latest Revisions | Discuss this page | Too simple to be simple Too simple to be simple Idea Examples Relationship to biased definitions Idea There is a general principle in mathematics that A trivial object is too simple to be simple. Quite often, classical references will define ‘simple’ (or an analogous term) in naïve way, so that a ‘trivial’ object is simple, but later it will become clear that more sophisticated theorems (especially classification theorems) work better if the de

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