MIT6_042JS10_lec07

MIT6_042JS10_lec07 - Axioms Mathematics for Computer...

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1 lec 3F.1 Albert R Meyer, February 19, 2010 Mathematics for Computer Science MIT 6.042J/18.062J Set Theory lec 3F.2 Albert R Meyer, February 19, 2010 Axioms x[x y x z] y = z Equality Power set x p s.s x s p lec 3F.3 Albert R Meyer, February 19, 2010 Russell’s Paradox Now let s be W , and reach a contradiction: lec 3F.4 Albert R Meyer, February 19, 2010 Disaster: Math is broken! I am the Pope, Pigs fly, and verified programs crash. .. lec 3F.5 Albert R Meyer, February 19, 2010 for all sets s …can only substitute W for s if W is a set ...but paradox is buggy Assumes that W is a set! lec 3F.6 Albert R Meyer, February 19, 2010 We can avoid the paradox, if we deny that W is a set! …which raises the key question: just which well-defined collections are sets? ...but paradox is buggy Assumes that W is a set!
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2 lec 3F.8 Albert R Meyer, February 19, 2010 Zermelo-Frankel Set Theory No simple answer, but the axioms of Zermelo-Frankel along with the Choice axiom
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This note was uploaded on 05/27/2011 for the course CS 6.042J taught by Professor Prof.albertr.meyer during the Spring '11 term at MIT.

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MIT6_042JS10_lec07 - Axioms Mathematics for Computer...

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