Search results for "03e10"

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Extended Natural Numbers and Counters

2020

Summary This article introduces extended natural numbers, i.e. the set ℕ ∪ {+∞}, in Mizar [4], [3] and formalizes a way to list a cardinal numbers of cardinals. Both concepts have applications in graph theory.

Applied Mathematics03e10 68v20Mathematics::General Topology020207 software engineeringNatural number0102 computer and information sciences02 engineering and technologysequence01 natural sciencesCombinatoricsComputational MathematicsMathematics::Logic010201 computation theory & mathematicscardinal0202 electrical engineering electronic engineering information engineeringextended natural numbersQA1-939MathematicsMathematicsSequence (medicine)MathematicsofComputing_DISCRETEMATHEMATICSFormalized Mathematics
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Natural Addition of Ordinals

2019

Summary In [3] the existence of the Cantor normal form of ordinals was proven in the Mizar system [6]. In this article its uniqueness is proven and then used to formalize the natural sum of ordinals.

natural sumApplied Mathematicshessenberg sumcantor normal form68t99ordinal numbersAlgebraMathematics::LogicComputational Mathematics03e1003b35QA1-939Natural (music)MathematicsMathematicsFormalized Mathematics
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