2,192 reputation
1426
bio website math.cornell.edu/~justin
location Ithaca, NY
age 39
visits member for 3 years, 5 months
seen Nov 10 '13 at 3:46
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).

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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
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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
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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.
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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
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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]).
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asked What is the effect of adding 1/2 to a continued fraction?
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Jan
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comment Usage of set theory in undergraduate studies
@ALC: Concerning your historical question, I don't know. I'm not a historian and what I could say would only be speculation. I think the notion that there could be independence of the sort that we now know exists would have been deeply shocking at the time and was, I believe, far from peoples minds. That said, the people at the turn of the century were certainly interested in trying to make some sort of rigorous definition of what mathematics was and what proof was. In light of Godel's works and Cohen's work (not to mention all of modern set theory), that was very much needed.
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comment Usage of set theory in undergraduate studies
@Toby: Sorry, but I don't know the first thing about ETCS.