lemma 7.54 Truncation error

open in the book · parts/02-mathematical-methods/05-real-analysis.tex:1158 · p. 220

Rests on

depends_on equation 7.31 eq:ana-e-series ¶
depends_on proposition 7.46 Geometric series ¶
- depends_on corollary A.46 Monotone convergence ¶
  - depends_on theorem A.40 Least-upper-bound property ¶
    - depends_on definition A.36 Cut ¶
    - depends_on definition A.38 Order on $\R$ ¶
      - depends_on definition A.36 Cut ¶ ↺
    - proves proof app:A-long-proofs@proof-29 ¶
  - proves proof app:A-long-proofs@proof-33 ¶
- 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 ¶ ↺
- proves proof ch:05-real-analysis@proof-27 ¶
proves proof ch:05-real-analysis@proof-34 ¶

Supports

depends_on corollary 7.55 The decimal expansion ¶
depends_on proposition 7.56 Irrationality ¶
- depends_on remark 7.94 Three numbers, two kinds ¶
depends_on remark 7.58 An identity, not a recipe ¶
- depends_on remark 7.70 What the condition says ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	eq:ana-e-series	declared	parts/02-mathematical-methods/05-real-analysis.tex:1164
`depends_on`	→	Geometric series	declared	parts/02-mathematical-methods/05-real-analysis.tex:1164
`depends_on`	←	The decimal expansion	declared	parts/02-mathematical-methods/05-real-analysis.tex:1196
`depends_on`	←	Irrationality	declared	parts/02-mathematical-methods/05-real-analysis.tex:1231
`depends_on`	←	An identity, not a recipe	declared	parts/02-mathematical-methods/05-real-analysis.tex:1316
`proves`	←	ch:05-real-analysis@proof-34	declared	parts/02-mathematical-methods/05-real-analysis.tex:1167