definition 3.38 Ordered pair and Cartesian product

open in the book · parts/02-mathematical-methods/01-logic-sets.tex:1074 · p. 29

ground object -- no derivation owed

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Supports

depends_on definition 3.23 Predicate ¶
- depends_on definition 3.24 Quantifiers ¶
  - depends_on definition 3.43 Map ¶
    - depends_on definition 4.2 Binary operation ¶
      - depends_on definition 4.3 Algebraic structure ¶
      - depends_on definition 4.4 Internal binary operation; magma ¶
    - depends_on definition 4.43 Group homomorphism ¶
      - depends_on definition 4.44 Group isomorphism ¶
      - depends_on definition 4.73 External semidirect product ¶
      - depends_on definition 5.141 Representation of a group ¶
      - depends_on proposition 4.42 When the homomorphisms form a group ¶
      - depends_on proposition 4.47 Image of the inverse element ¶
      - depends_on proposition 4.46 Image of the neutral element ¶
      - depends_on proposition 4.17 Trivial kernel of a homomorphism ¶
    - depends_on definition 4.16 Image ¶
    - depends_on definition 7.9 Real function ¶
      - depends_on definition 7.15 Absolute-value function ¶
      - depends_on definition 7.13 Composite function ¶
      - depends_on definition 7.10 Constant function ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.12 Product of functions ¶
      - depends_on definition 7.11 Sum of functions ¶
    - depends_on definition 6.24 Metric ¶
      - depends_on definition 7.140 Hausdorff measure ¶
      - depends_on definition 16.12 The two norms; weak and strong neighbourhoods ¶
      - depends_on definition 5.22 Metric associated with a norm ¶
      - depends_on definition 10.24 Well-posed problem ¶
      - depends_on definition 6.27 Convergence; Cauchy sequence; completeness ¶
      - depends_on definition 6.26 Open ball; metric topology ¶
      - depends_on definition 6.29 Sequential compactness ¶
      - depends_on lemma A.505 A continuous partition of unity ¶
depends_on definition 6.24 Metric ¶ ↺
depends_on proposition 3.67 Countability of the plane of naturals ¶
- depends_on corollary 3.68 The rationals are countable ¶
  - depends_on corollary A.3 The continuum is the power set of the naturals ¶
  - depends_on corollary 3.70 cor:inf-irrationals-uncountable ¶
  - depends_on remark 7.94 Three numbers, two kinds ¶
- depends_on lemma 7.139 A countable union of null sets is null ¶
  - depends_on proposition 7.143 The Hausdorff dimension never exceeds the box dimension ¶
  - depends_on proposition 7.141 The critical exponent, and the Hausdorff dimension ¶
    - depends_on proposition 7.143 The Hausdorff dimension never exceeds the box dimension ¶ ↺
  - depends_on remark 7.94 Three numbers, two kinds ¶ ↺
- depends_on lemma A.6 Lindenbaum ¶
- depends_on remark 7.94 Three numbers, two kinds ¶ ↺

Neighborhood

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Edges

type	direction	node	provenance	where
`depends_on`	←	Predicate	declared	parts/02-mathematical-methods/01-logic-sets.tex:622
`depends_on`	←	Metric	declared	parts/02-mathematical-methods/04-topology.tex:500
`depends_on`	←	Countability of the plane of naturals	declared	parts/02-mathematical-methods/01-logic-sets.tex:1697