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a home page for the Axiom of Choice:http://www.math.vanderbilt.edu/~schectex/ccc/choice.html

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The Axiom of Choice

The Axiom of Choice by Thomas J. Jech Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths and consequences of the axiom of choice. Each chapter contains several problems, graded according to difficulty, and concludes with some historical remarks.An introduction to the use of the axiom of choice is followed by explorations of consistency, permutation models, and independence. Subsequent chapters examine embedding...

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Axiom Of Choice - Beyond Denial

Axiom Of Choice - Beyond Denial, Blue

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How the Axiom of Choice can lead to this paradox regarding our notions of volume is that the axiom allows for the construction of non-measurable sets. This decomposition and reconstruction cannot be done in the physical world, because if you take and apple and cut it up into pieces with a knife, each of these pieces is “measurable.” That is, they have boundaries and a sense of volume, whereas the sets constructed using the Axiom of Choice do not obey these properties.

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Jurgita Dronina and Isaac Hernández “Axiom of Choice” (Ernst Meisner) from “Back to Bach”, Het Nationale Ballet (The Dutch National Ballet) - Photographer Angela Sterling

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