Talk:Closure with a twist

Nonsense?

This article currently makes no sense at all. Perhaps by "transposed" the writer means "complemented", but how does he get 110 + 110 = 000? Even in binary, that doesn't work. (110 + 110 is 1100, or 100 modulo 2³.) And then even if we accept that by "+" he means "XOR", we're still left with

   F = {000,110,101}

   F + 110 = {110,000,011} = F 

which is clearly not true unless we're willing to accept that 011 = 101.

This obviously isn't a hoax, since it's copied pretty much verbatim from http://www.cwatsets.org/ (and BTW it might be a copyright violation to copy that site, but it makes so little sense that I don't care) — but what on earth does it mean?

The article could probably be greatly improved by giving an example of a set which is a group, or which is a cwatset. (Are the two terms synonymous? Does one imply the other? Or else what's that talk about groups closed under addition?) If the article isn't cleaned up in a few days, I'll nominate it for deletion, just to get it out of the way. --Quuxplusone 07:20, 8 February 2007 (UTC)

The addition is modulo two. We don't have to accept the equation 011 = 101; we just have to define 1 + 1 = 0, and then 01 = 01. I don't think a group ought to be defined here … there's a link in the article, and that should be sufficient. Finally, the article as it stands seems quite clear to me ... every group of order 2ⁿ is a cwatset (ok, it's isomorphic to a cwatset), but not every cwatset is a group. I agree that the article could stand to be wikified, but deletion seems a bit extreme. DavidCBryant 13:12, 20 March 2007 (UTC)