By Jiří Lebl.
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Online text: www.jirka.org/ra/html/sec_rint.html
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Online text: www.jirka.org/ra/html/sec_seqsandlims.html
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Cited passages: Lebl, Basic Analysis I, §1.2: approximation of a supremum; Lebl, Basic Analysis I, §1.2: supremum, infimum and attainment.
Online text: www.jirka.org/ra/html/sec_bw.html
Cited passages: Basic Analysis, Volume I by Jiří Lebl, opening footnote to §2.3: the theorem's two namesakes; Basic Analysis, Volume I by Jiří Lebl, §2.3.3, Theorem 2.3.8: every bounded real sequence has a convergent subsequence; Lebl, Basic Analysis I, §2.3: equality of finite bounds and extended limits; Lebl, Basic Analysis I, §2.3: extreme subsequential limits.
Online text: www.jirka.org/ra/html/sec_puconv.html
Cited passages: Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.1.1, Definition 6.1.1 and Proposition 6.1.5; Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.1.1, Example 6.1.2, even powers on the interval from minus one to one; Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.1.2, Definition 6.1.6 and Proposition 6.1.7.
Online text: www.jirka.org/ra/html/sec_liminter.html
Cited passages: Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.2.1, Theorem 6.2.2; Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.2.2, Theorem 6.2.4; Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.2.3, Theorem 6.2.10 and the unbounded-interval observation following its proof.
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