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rjlipton.com | ||
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njwildberger.com
There are several approaches to the modern theory of "real numbers". Unfortunately, none of them makes complete sense. One hundred years ago, there was vigorous discussion about the ambiguities with them and Cantor's theory of "infinite sets". As time went by, the debate subsided but the difficulties didn't really go away. A largely unquestioning uniformity... |
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almostsuremath.com
Probability and measure theory relies on the concept of measurable sets. On the real numbers ?, in particular, there are several different sigma-algebras which are commonly used, and a set is said to be measurable if it lies in the one under consideration. Probabilities and measures are only defined for events lying in a specific... |
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existentialtype.wordpress.com
It is well-known that constructivists renounce "proof by contradiction", and that classicists scoff at the critique. "Those constructivists," the criticismgoes, "want to rule out proofs by contradiction. How absurd! Look, Pythagoras showed that the square root of two is irrational by deriving a contradiction from the assumption that it is rational. There is nothing wrong... |
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www.cambridge.org
Combinatorial and harmonic-analytic methods for integer tilings - Volume 10 |
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