113 reputation
5
bio website
location
age
visits member for 2 years
seen Nov 27 '12 at 5:49

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