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Lieferstatus:	i.d.R. innert 7-14 Tagen versandfertig
Veröffentlichung:	Mai 2026
Genre:	Schulbücher
	Brouwer's Fixed Point Theorem / Choice sequences / Constructive analysis / Constructive logic / constructive mathematics / Constructive real numbers / Constructivism in mathematics / Creating Subject / Creative Subject / foundations of mathematics / Intuitionism in mathematics / Intuitionistic Logic / Intuitionistic mathematics / L.E.J. Brouwer / Philosophy of Mathematics / Proof Theory and Constructive Mathematics / Weak counterexamples mehr...
ISBN:	9783032164902
EAN-Code:	9783032164902
Verlag:	Springer International Publishing
Einband:	Kartoniert
Sprache:	English
Dimensionen:	H 235 mm / B 155 mm / D
Seiten:	167
Illustration:	XIV, 167 p. 45 illus., schwarz-weiss Illustrationen
Zus. Info:	EUDR exemption - product or manufacturing materials placed on the market prior to 31.12.2025.
Bewertung:	Titel bewerten / Meinung schreiben

Inhalt:

This book introduces the core ideas of L.E.J. Brouwer’s approach to constructivity in mathematics, focusing on analysis, set theory, and topology, while considering his philosophical motivations. Brouwer’s "intuitionism" offers a coherent alternative to classical (nonconstructive) mathematics. Starting with the rejection of the Principle of the Excluded Middle, the book reconstructs number systems and analysis using Cauchy sequences. It compares constructive and classical methods, highlights where classical theorems fail through "weak counterexamples", and examines Brouwer’s classical and constructive versions of the Fixed-Point Theorem. Intuitionistic concepts like choice sequences and the Creating Subject lead to surprising results, such as the continuity of all total real functions and the existence of effective but non-recursive functions. Brief but fundamental comparisons are made with the later alternatives of Markov and Bishop. Intended as an introduction for undergraduates, this book is suitable for mathematics students interested in philosophy as well as philosophers with some mathematical background.