bio | website | math.cornell.edu/~justin |
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location | Ithaca, NY | |
age | 40 | |
visits | member for | 3 years, 11 months |
seen | Aug 24 at 19:40 | |
stats | profile views | 2,785 |
I'm a set theorist working at Cornell. Most of my work has been with forcing axioms and the combinatorics and Ramsey theory of the first uncountable cardinal. I am also interested in ways in which set theory can be applied to other areas of mathematics. Additionally, I have interests in group theory (amenability in particular).
Jul 2 |
awarded | Curious |
May 15 |
accepted | What is the effect of adding 1/2 to a continued fraction? |
May 15 |
comment |
What is the effect of adding 1/2 to a continued fraction?
Noam, thanks. I've been away from MO for a while, but this was actually exactly what I was looking for. |
May 13 |
awarded | Popular Question |
May 12 |
awarded | Good Question |
Jan 8 |
awarded | Popular Question |
Jan 3 |
awarded | Nice Answer |
Nov 12 |
awarded | Yearling |
Oct 18 |
awarded | Guru |
Oct 15 |
awarded | Nice Answer |
Aug 8 |
awarded | Necromancer |
Jun 25 |
awarded | Revival |
Apr 30 |
comment |
What is the effect of adding 1/2 to a continued fraction?
@Douglas: Could you contact me off list? |
Apr 30 |
comment |
What is the effect of adding 1/2 to a continued fraction?
@Douglas: Actually you might be right. The formula in my comment is a little cleaner though. |
Apr 30 |
comment |
What is the effect of adding 1/2 to a continued fraction?
@Douglas: The cases depending on whether a1 > 1 seems off. I think the (or rather a) formula is 1/2 x = [a0/2,2x'] or [(a0-1)/2,1,1,(x'-1)/2] (depending on parity of a0) and 2x=[2a0,x'/2]. This gives x/2 = [a0/2,2a1,x''/2] or [(a0-1)/2,1,1,(x'-1)/2]. Thanks again; this was exactly what I was looking for. I had dismissed finding a rule this simple for some reason. |
Apr 29 |
comment |
What is the effect of adding 1/2 to a continued fraction?
@Douglas: Check your formula for doubling. I think it is not quite correct. |
Apr 26 |
comment |
What is the effect of adding 1/2 to a continued fraction?
@Douglas: thanks, but this is not really what I'm asking. The 2[a0;2a1,a2,2a3,a4,...]=[2a0;a1,2a2,a3,2a4,...] part is in the spirit of what I want, but I want something analogous which works for any sequence. I was aware of this observation --- the hard part is of course in dealing with the remainders. |
Apr 26 |
comment |
What is the effect of adding 1/2 to a continued fraction?
Thanks, but this is not really what I'm asking. See the comments in the edit portion of the question. |
Apr 26 |
revised |
What is the effect of adding 1/2 to a continued fraction?
added the "edit:" part of the text |
Apr 26 |
comment |
What is the effect of adding 1/2 to a continued fraction?
@David:Actually I think this is not quite true. Unless I am missing something, this is not reversible. You can, however, multiply by 4 by adding 1/2 and reciprocating though. The point is that multiplication by 1/2 corresponds to operations in PSL_2(Z[1/sqrt(2)]), while adding 1/2 comes from PSL_2(Z[1/2]). |