Comments on: Spot The Not http://yaniv.leviathanonline.com/blog/riddles/spot-the-not/ Strain your Brain Tue, 13 Sep 2011 13:21:47 -0700 hourly 1 http://wordpress.org/?v=3.1 By: Seb Przd http://yaniv.leviathanonline.com/blog/riddles/spot-the-not/comment-page-1/#comment-251 Seb Przd Wed, 31 Oct 2007 15:56:53 +0000 http://yaniv.leviathanonline.com/blog/riddles/spot-the-not/#comment-251 I agree with the poster above. The boundary of a union is not necessarily the union of the boundaries, and the Cantor set (well, its complement) is a good example. Claim 4 is not very constructive... the intersection of the irrationals with a fat Cantor set? I agree with the poster above. The boundary of a union is not necessarily the union of the boundaries, and the Cantor set (well, its complement) is a good example. Claim 4 is not very constructive… the intersection of the irrationals with a fat Cantor set?

]]> By: yaniv http://yaniv.leviathanonline.com/blog/riddles/spot-the-not/comment-page-1/#comment-249 yaniv Wed, 31 Oct 2007 15:10:08 +0000 http://yaniv.leviathanonline.com/blog/riddles/spot-the-not/#comment-249 You are of course right. You are of course right.

]]> By: Seb Przd http://yaniv.leviathanonline.com/blog/riddles/spot-the-not/comment-page-1/#comment-248 Seb Przd Wed, 31 Oct 2007 15:06:40 +0000 http://yaniv.leviathanonline.com/blog/riddles/spot-the-not/#comment-248 Is the definition of boundary correct? it seems it should be bdy(A) is the set { x | for all e>0, (x-e,x+e) contains both a point from A and from R-A }. Is the definition of boundary correct? it seems it should be
bdy(A) is the set { x | for all e>0, (x-e,x+e) contains both a point from A and from R-A }.

]]> By: ury http://yaniv.leviathanonline.com/blog/riddles/spot-the-not/comment-page-1/#comment-70 ury Tue, 14 Aug 2007 18:51:14 +0000 http://yaniv.leviathanonline.com/blog/riddles/spot-the-not/#comment-70 Claim 7 is wrong. Consider the Cantor Set as a counter-example and show that claim 8 is wrong, then deduce that claim 7 must be wrong as well. In reality, one can only prove the following: Given a family of open and disjoint sets, the following holds: union[ boundary[Ai] ] "is a subset of" boundary[ union[Ai] ] Perform Claim 7 is wrong. Consider the Cantor Set as a counter-example and show that claim 8 is wrong, then deduce that claim 7 must be wrong as well.

In reality, one can only prove the following:
Given a family of open and disjoint sets, the following holds:
union[ boundary[Ai] ] “is a subset of” boundary[ union[Ai] ]

Perform

]]>