Tag: aleph null

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…

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…

Cosmologists’ problems with alephnull 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. Alephnull () 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…

“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:…