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Talk:Algorithmically random sequence

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This is an old revision of this page, as edited by 82.35.28.217 (talk) at 13:40, 27 July 2006. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

RAND is Sigma^0_2

It is correct to say that RAND is Sigma^0_2, because there is a Sigma^0_2 formula that defines the class of 1-random real numbers. It is not true that every random real is itself Sigma^0_2; there are 1-random reals of arbitrarily high Turing degree. CMummert 23:41, 23 June 2006 (UTC)[reply]

Edit today

Here are some comments on the changes I made today

  • It is not NPOV to describe some things are very technical and describe other things as very easy. My impressions of easy and hard are in fact the opposite of the opinions the article used to have. In any event, there is no reason to lecture the reader about how hard some idea is. I removed all such comments.
  • I rewrote the Martin-Löf definition in topological language, which should be more clear.
  • I made other small changes.

CMummert 14:00, 24 June 2006 (UTC)[reply]

Lebesgue measure

I don't think it's proper to call the measure of a cylinder Lebesgue measure. A cylinder isn't a subset of R^n. It's not internally consistent even with Wikipedia's current definition of Lebesgue measure. ~~

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