Tag: aleph null
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Subsets of the continuum
Following on from the discussion of the set of all the integers, with order , and the set of all its subsets– the continuum, of order with – what can we say about the set of all subsets of the continuum? Like any other set of order we can say it has order , in this…
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The maths of the spirograph… with the drawings
Well, I sat down and thought this was going to be easy, but it has taken me three hours to work the maths of a smaller inner wheel rolling around inside a large outer wheel: mainly because for the first two of those I neglected the basic insight that the inner wheel rolls in the…
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Cosmologists’ problems with aleph-null and the multiverse
This is another insight from Brian Greene’s book The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos – well worth reading. Aleph-null () is the order (size) of the set of countably infinite objects. The counting numbers are the obvious example: one can start from one and keep on going. But any…
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“Basically, you would be able to compute anything you wanted”
The quote that forms the title here comes from Lance Fortnow, a computer scientist at Northwestern University, in an article (here – subscription required) in the current edition of the New Scientist on the question. It’s an odd statement for a computer scientist to make – most numbers are transcendental numbers and so are fundamentally incomputable:…
cartesian product ... stuff about computing mostly 