axiom 3.33 Peano axioms

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Supports

• depends_on definition 3.83 Peano arithmetic ¶
  • depends_on lemma A.19 Numerals behave ¶
    • depends_on lemma A.24 lem:app-inc-beta-delta0 ¶
      • depends_on theorem A.25 thm:app-inc-primrec ¶
        • depends_on theorem A.17 Representability ¶
    • depends_on lemma A.20 $\Sigma_{1}$-completeness ¶
      • depends_on theorem A.25 thm:app-inc-primrec ¶ ↺
      • depends_on theorem A.17 Representability ¶ ↺
    • depends_on theorem A.25 thm:app-inc-primrec ¶ ↺
    • depends_on theorem A.27 Rosser ¶
  • depends_on lemma 3.86 Diagonal lemma ¶
    • depends_on theorem 3.87 Gödel, 1931 ¶
      • depends_on theorem A.29 Second incompleteness theorem ¶
      • depends_on theorem 3.88 Gödel's second incompleteness theorem ¶
    • depends_on theorem 3.91 Tarski's undefinability of truth ¶
  • depends_on theorem 3.88 Gödel's second incompleteness theorem ¶ ↺
• depends_on definition 3.65 Countable set ¶
  • 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 definition 7.138 Set of measure zero ¶
    • depends_on definition 7.140 Hausdorff measure ¶
      • depends_on definition 7.142 Box-counting dimension ¶
        • depends_on definition 32.79 Box-counting dimension, restated from Part II ¶
        • depends_on proposition 7.143 The Hausdorff dimension never exceeds the box dimension ¶
        • depends_on remark 7.144 What is developed here, and what is not ¶
      • 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 7.144 What is developed here, and what is not ¶ ↺
    • 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 remark 7.94 Three numbers, two kinds ¶ ↺
    • depends_on proposition 7.141 The critical exponent, and the Hausdorff dimension ¶ ↺
    • depends_on remark 7.144 What is developed here, and what is not ¶ ↺
  • depends_on proposition 3.67 Countability of the plane of naturals ¶
    • depends_on corollary 3.68 The rationals are countable ¶ ↺
    • depends_on lemma 7.139 A countable union of null sets is null ¶ ↺
    • depends_on lemma A.6 Lindenbaum ¶
    • depends_on remark 7.94 Three numbers, two kinds ¶ ↺
  • depends_on theorem 3.69 Uncountability of the continuum ¶
    • depends_on corollary 3.70 cor:inf-irrationals-uncountable ¶ ↺
    • depends_on remark 7.94 Three numbers, two kinds ¶ ↺
• depends_on lemma 7.65 The integer part ¶
  • depends_on lemma 7.67 The limit over real exponents ¶
    • depends_on proposition 7.68 The natural base ¶
      • depends_on remark 7.70 What the condition says ¶
  • depends_on proposition 7.77 Special values, periodicity, and the kernel ¶
    • depends_on lemma 7.78 Chord, arc, tangent ¶
      • depends_on proposition 7.79 The polygon recursion ¶
        • depends_on corollary 7.81 The decimal expansion of $\pi$ ¶
        • depends_on proposition 7.83 Viète's product ¶
        • depends_on remark 7.82 What Archimedes proved ¶
        • depends_on remark 7.80 Why these are the polygon perimeters ¶
        • depends_on remark 7.84 One construction, two faces ¶
    • depends_on proposition 7.85 Irrationality of $\pi$ ¶
      • depends_on remark 7.94 Three numbers, two kinds ¶ ↺
      • depends_on remark 7.87 Priority, and what irrationality does not give ¶
    • depends_on proposition 7.79 The polygon recursion ¶ ↺
    • depends_on proposition 7.83 Viète's product ¶ ↺
    • depends_on proposition 125.2 Crystallographic restriction ¶
      • depends_on remark 125.3 What the theorem does and does not forbid ¶
    • depends_on remark 7.88 $\pi$ elsewhere in this treatise ¶
  • depends_on proposition 7.89 Irrationality of square roots ¶
    • depends_on proposition 7.91 The golden ratio ¶
      • depends_on proposition 7.92 Continued fraction and the Fibonacci ratios ¶
        • depends_on remark 7.95 Where $\varphi$ is used ¶
      • depends_on proposition 125.2 Crystallographic restriction ¶ ↺
      • depends_on remark 7.95 Where $\varphi$ is used ¶ ↺
      • depends_on remark 7.94 Three numbers, two kinds ¶ ↺
• depends_on lemma 7.64 Well-ordering of $\N$ ¶
  • depends_on lemma 7.65 The integer part ¶ ↺
  • depends_on proposition 7.89 Irrationality of square roots ¶ ↺