fmkatz
Reputation
Next privilege 125 Rep.
Vote down
 Nov 7 comment Self-similarity in ultrafilters over N How can $[2n]_Y=X$ if X contains the odd numbers? $[2n]_Z$ is always a subset of the even numbers. Nov 7 comment Self-similarity in ultrafilters over N Sorry, I was going down the wrong path, there. Do you have a reference for the general theorem about fixed points? Thanks. Nov 7 comment Self-similarity in ultrafilters over N Welcome, indeed. There is probably noone better suited to answer this question. But, perhaps I need to clarify the notation. Nov 4 accepted Half the rationals? Nov 3 comment Half the rationals? Wow. Thank you. That's the kind of explicit solution I was hoping for - though, I must admit, it will take me a while to work through and understand the proof. (The proof certainly has enough detail; I'm just weak on the number theory.) Nov 3 awarded Supporter Nov 3 comment Self-similarity in ultrafilters over N I am trying to prove the existence of sizings of sets of natural numbers which have satisfy some similarity conditions - for example - that $$\sigma(X) = \sigma(Y) \iff \sigma([kn]_X) =\sigma([kn]_Y)$$. By sizings, I mean the kinds of orderings developed in the citations on my answer to math.stackexchange.com/questions/1393/…. Nov 3 asked Self-similarity in ultrafilters over N Nov 1 comment Half the rationals? Both answers provide the set requested - and generalize nicely. I would still like to know whether there's a solution with a more explicit definition of the set - along the lines of ChristopherA.Wong's or @EstebanCrespi 's comments, but with a proof or reference to why they work. Nov 1 awarded Scholar Nov 1 revised Half the rationals? Missed an x Nov 1 comment Half the rationals? Thank you, Qiaochu Yuan. Nov 1 revised Half the rationals? Set variables now in upper case. Thank you. Nov 1 awarded Student Nov 1 asked Half the rationals? Oct 15 answered Set theory - proving cardinalities of two non-disjunct sets Oct 13 answered About the notation of “there exist” and “For all” Sep 28 awarded Teacher Sep 28 awarded Editor Sep 28 revised Relative sizes of sets of integers and rationals revisited - how do I make sense of this? added 16 characters in body