remark 7.58 An identity, not a recipe

open in the book · parts/02-mathematical-methods/05-real-analysis.tex:1291 · p. 222

remark -- no derivation owed by its kind

Rests on

depends_on equation 7.38 eq:ana-e-binomial ¶
depends_on lemma 7.54 Truncation error ¶
- 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 $\R$ ¶
      - 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 ¶
depends_on proposition 7.57 The limit definition ¶
- depends_on definition 7.53 $\ee$ ¶
  - depends_on definition 7.45 Series ¶ ↺
  - depends_on proposition 7.48 Ratio test ¶
    - depends_on proposition 7.47 Comparison; absolute convergence ¶
      - depends_on corollary A.46 Monotone convergence ¶ ↺
      - depends_on definition 7.45 Series ¶ ↺
      - depends_on theorem 7.8 Cauchy criterion ¶
      - proves proof ch:05-real-analysis@proof-28 ¶
    - depends_on proposition 7.46 Geometric series ¶ ↺
    - depends_on theorem 7.8 Cauchy criterion ¶ ↺
    - proves proof ch:05-real-analysis@proof-29 ¶
- depends_on equation 5.3 eq:lin-binomial ¶
- depends_on proposition 7.6 Algebra of limits ¶
  - depends_on definition 7.4 Convergence ¶ ↺
  - depends_on proposition 7.3 Triangle inequality ¶
    - depends_on definition 7.2 Absolute value ¶ ↺
    - proves proof ch:05-real-analysis@proof-1 ¶
  - proves proof ch:05-real-analysis@proof-3 ¶
- proves proof ch:05-real-analysis@proof-37 ¶

Supports

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-binomial	declared	parts/02-mathematical-methods/05-real-analysis.tex:1316
`depends_on`	→	Truncation error	declared	parts/02-mathematical-methods/05-real-analysis.tex:1316
`depends_on`	→	The limit definition	declared	parts/02-mathematical-methods/05-real-analysis.tex:1316
`depends_on`	←	What the condition says	declared	parts/02-mathematical-methods/05-real-analysis.tex:1729