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  2. Gödel's incompleteness theorems - Wikipedia

    en.wikipedia.org/wiki/Gödel's_incompleteness...

    The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e. an algorithm ) is capable of ...

  3. Proof sketch for Gödel's first incompleteness theorem

    en.wikipedia.org/wiki/Proof_sketch_for_Gödel's...

    The sketch here is broken into three parts. In the first part, each formula of the theory is assigned a number, known as a Gödel number, in a manner that allows the formula to be effectively recovered from the number.

  4. List of incomplete proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_incomplete_proofs

    The first complete proofs were given by Marcel-Paul Schützenberger in 1977 and Thomas in 1974. Class numbers of imaginary quadratic fields. In 1952 Heegner published a solution to this problem. His paper was not accepted as a complete proof as it contained a gap, and the first complete proofs were given in about 1967 by Baker and Stark. In ...

  5. Comparison theorem - Wikipedia

    en.wikipedia.org/wiki/Comparison_theorem

    In the theory of differential equations, comparison theorems assert particular properties of solutions of a differential equation (or of a system thereof), provided that an auxiliary equation/inequality (or a system thereof) possesses a certain property. Differential (or integral) inequalities, derived from differential (respectively, integral ...

  6. Category:Comparison (mathematical) - Wikipedia

    en.wikipedia.org/wiki/Category:Comparison...

    Often, a distance (for comparison) is calculated by subtraction (in some metric space), but comparison can be based on arbitrary orderings that don't support subtraction or the notion of distance. Moreover, comparison circuitry doesn't belong in a purely mathematical or computing category.

  7. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    Complete coloring, a.k.a. achromatic number [3]: GT5 Cycle rank; Degree-constrained spanning tree [3]: ND1 Domatic number [3]: GT3 Dominating set, a.k.a. domination number [3]: GT2 NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in

  8. Comparability - Wikipedia

    en.wikipedia.org/wiki/Comparability

    Hasse diagram of the natural numbers, partially ordered by "x≤y if x divides y".The numbers 4 and 6 are incomparable, since neither divides the other. In mathematics, two elements x and y of a set P are said to be comparable with respect to a binary relation ≤ if at least one of x ≤ y or y ≤ x is true.

  9. Completeness - Wikipedia

    en.wikipedia.org/wiki/Completeness

    Complete search algorithm, a search algorithm that is guaranteed to find a solution if there is one Incomplete database , a compact representation of a set of possible worlds Music