Tag: Continuum Hypothesis
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Another way of looking at the alephs
This is another insight gained from Wheels, Life and Other Mathematical Amusements– this time about the transfinite numbers. The smallest transfinite number, so -called is that of the countable infinity, or the counting numbers (the integers). Start at 1 (or 0) and keep going. But how many sets can one make from the counting numbers?…
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The wheels of Aristotle
Sometimes you come across a thing where beauty matches simplicity, and Aristotle’s Wheel Paradox is just such a thing. I came across it this afternoon after I returned to London from two too-short weeks away and a second-hand book I’d ordered, Wheels, Life and Other Mathematical Amusements, based on Martin Gardner‘s columns for the Scientific…
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“Ultimate L” explained
Well, that is what I wanted to write about – Hugh Woodin‘s theories of infinity, and indeed I found a blog that discussed a lot of this – http://caicedoteaching.wordpress.com/2010/10/19/luminy-hugh-woodin-ultimate-l-i/ But that is somewhat beyond me! And there does not appear to be a wikipedia article on this, so you may have to wait for some…
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The importance of Turing’s findings
Yesterday I was speaking to a friend – who knows about computers but not about computer science – who told me this blog was just too difficult: so I thought I’d seek to order my own thoughts after reading The Annotated Turing and assist humanity in general (!) by writing a piece that explains what…
cartesian product ... stuff about computing mostly 