Tag: Continuum Hypothesis

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?…

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 tooshort weeks away and a secondhand book I’d ordered, Wheels, Life and Other Mathematical Amusements, based on Martin Gardner‘s columns for the Scientific…

“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/luminyhughwoodinultimateli/ 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…

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…