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definition: निर्धारण परिभाषा | |
impredicative definition meaning in Hindi
impredicative definition sentence in HindiExamples
More: Next- Poincar?and Weyl argued that impredicative definitions are problematic only when one or more underlying sets are infinite.
- Set theories such as ZFC are not based on this sort of predicative framework, and allow impredicative definitions.
- Then to exclude impredicative definitions within a type, the types above type 0 are further separated into orders.
- But this separation into orders makes it impossible to construct the familiar analysis, which [ see Kleene's example at Impredicativity ] contains impredicative definitions.
- This notion of collection-or or class-as-object, when used without restriction, results in Russell's paradox; see more below about impredicative definitions.
- Kleene observes that " to exclude impredicative definitions within a type, the types above type 0 [ primary objects or individuals " not subjected to logical analysis " ] are further separated into orders.
- If only definable properties are considered to exist, then the axiom means that to every impredicative definition within a given type there is an equivalent predicative one ( Kleene 1952 : 44 45 ).
- He gives two examples of impredicative definitions & ndash; ( i ) the notion of Dedekind chains and ( ii ) " in analysis wherever the maximum or minimum of a previously defined " completed " set of numbers } } is used for further inferences.
- Zermelo's example of minimum and maximum of a previously defined " completed " set of numbers reappears in Kleene 1952 : 42-42 where Kleene uses the example of Least upper bound in his discussion of impredicative definitions; Kleene does not resolve this problem.
- G�del's approach to the law of excluded middle was to assert that objections against " the use of'impredicative definitions'" " carried more weight " than " the law of excluded middle and related theorems of the propositional calculus " ( Dawson p . 156 ).