proposition 7.56 Irrationality

open in the book · parts/02-mathematical-methods/05-real-analysis.tex:1226 · p. 221

Rests on

depends_on definition 7.53 $\ee$ ¶
- depends_on definition 7.45 Series ¶
  - depends_on definition 7.2 Absolute value ¶
  - depends_on definition 7.4 Convergence ¶
    - depends_on definition 7.2 Absolute value ¶ ↺
- depends_on proposition 7.48 Ratio test ¶
  - depends_on proposition 7.47 Comparison; absolute convergence ¶
    - depends_on corollary A.46 Monotone convergence ¶
      - depends_on theorem A.40 Least-upper-bound property ¶
      - proves proof app:A-long-proofs@proof-33 ¶
    - depends_on definition 7.45 Series ¶ ↺
    - depends_on theorem 7.8 Cauchy criterion ¶
      - depends_on corollary A.47 Cauchy completeness ¶
      - depends_on definition 7.4 Convergence ¶ ↺
      - proves proof ch:05-real-analysis@proof-5 ¶
    - proves proof ch:05-real-analysis@proof-28 ¶
  - depends_on proposition 7.46 Geometric series ¶
    - depends_on corollary A.46 Monotone convergence ¶ ↺
    - depends_on definition 7.45 Series ¶ ↺
    - proves proof ch:05-real-analysis@proof-27 ¶
  - depends_on theorem 7.8 Cauchy criterion ¶ ↺
  - proves proof ch:05-real-analysis@proof-29 ¶
depends_on lemma 7.54 Truncation error ¶
- depends_on equation 7.31 eq:ana-e-series ¶
- depends_on proposition 7.46 Geometric series ¶ ↺
- proves proof ch:05-real-analysis@proof-34 ¶
proves proof ch:05-real-analysis@proof-36 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	$\ee$	declared	parts/02-mathematical-methods/05-real-analysis.tex:1231
`depends_on`	→	Truncation error	declared	parts/02-mathematical-methods/05-real-analysis.tex:1231
`depends_on`	←	Three numbers, two kinds	declared	parts/02-mathematical-methods/05-real-analysis.tex:2849
`proves`	←	ch:05-real-analysis@proof-36	declared	parts/02-mathematical-methods/05-real-analysis.tex:1234