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Unformatted text preview: 3 If every real number was algebraic then, R = A R would be countable. We have shown in class that R is not countable, so R A and hence there must be a non-algebraic real number; indeed there must be an uncountably innite set of them. (3) Rudin, Chapter 2, Problem 4 We have shown in class that the set of rational numbers, Q R is countable. Since R is uncountable it cannot be equal to Q so there must exist irrational real numbers. 1...
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This note was uploaded on 12/16/2011 for the course STAT 5446 taught by Professor Frade during the Fall '09 term at FSU.
- Fall '09