Mathematical Analysis

Apostol, T. M. (1974). Mathematical Analysis. Addison-Wesley.

Type

Book

Intellectual base

Textbook

Year

1974

Link

https://archive.org/details/mathematicalanal0000apos

Cited from

mathematics

Cited by

5 citations across 5 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Boundedness
  • Boundedness is not the same as convergence, as Apostol (1974) develops in his treatment of bounded sequences and the Bolzano-Weierstrass theorem.

    This sourcedevelops the Bolzano-Weierstrass theorem (every bounded sequence in R^n has a convergent subsequence), emphasizing boundedness as the essential hypothesis distinguishing it from convergence.

Domain-specific

• Finite set
  • … bijection to an initial finite ordinal, cardinality including zero, equivalent induction and Dedekind criteria, subsets, unions and products, and contrast with infinite sets are explicit. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• Improper integral
  • … truncation parameters, proper subintegrals, one-sided independent limits, finite convergence criterion, absolute or conditional status and distinction from Cauchy principal value are explicit. to An applied instance preserves the invariant under changed notation, scale, dataset, jurisdiction, or implementation..
• Real-valued function
  • A real-valued function assigns exactly one real number to each element of its declared domain, which may itself be arbitrary rather than real.
• Root Test
  • It does not prove divergence merely because \(L=1\): both \(\sum1/n\) and \(\sum1/n^2\) have root-test value one.

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