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March 2010
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set theory

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Tags: set theory : foundations of mathematics : Barber's Paradox : Russell's Paradox : Theory of Types : Zermelo-Fraenkel axiomatisation of set theory


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Richard Elwes continues his investigation into Cantor and Cohen's work. He investigates the continuum hypothesis, the question that caused Cantor so much grief.

Tags: history of mathematics : axiom : logic : set theory : Zermelo-Fraenkel axiomatisation of set theory : hilbert problems : infinity : continuum hypothesis


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What's the nature of infinity? Are all infinities the same? And what happens if you've got infinitely many infinities? In this article Richard Elwes explores how these questions brought triumph to one man and ruin to another, ventures to the limits of mathematics and finds that, with infinity, you're spoilt for choice.

Tags: history of mathematics : axiom : logic : set theory : Russell's Paradox : Zermelo-Fraenkel axiomatisation of set theory : infinity : axiom of choice