lemma A.37 Elementary properties of cuts

open in the book · appendices/A-long-proofs.tex:2916 · p. 2809

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lemma A.37: Elementary properties of cutsA.37definition A.36: CutA.36lemma A.42: (ℝ, +) is an ordered abelian groupA.42lemma A.39: The order is totalA.39proof : app:A-long-proofs@proof-27proofcorollary A.45: Archimedean property and density of ℚA.45definition A.41: AdditionA.41definition A.43: MultiplicationA.43definition A.38: Order on ℝA.38theorem A.40: Least-upper-bound propertyA.40lemma A.44: ℝ is an ordered fieldA.44proof : app:A-long-proofs@proof-30proofproof : app:A-long-proofs@proof-28proof

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typedirectionnode provenancewhere
depends_on Cut declared appendices/A-long-proofs.tex:2919
depends_on $(\R, +)$ is an ordered abelian group declared appendices/A-long-proofs.tex:3005
depends_on The order is total declared appendices/A-long-proofs.tex:2943
proves app:A-long-proofs@proof-27 declared appendices/A-long-proofs.tex:2922