197 reputation
128
bio website math.uchicago.edu/~ded
location University of Chicago
age 31
visits member for 4 years, 11 months
seen Oct 24 '12 at 7:03
I am a graduate student studying mathematical logic. My research interests include computability theory and effective randomness.

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awarded  Popular Question
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awarded  Popular Question
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awarded  Nice Question
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awarded  Yearling
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awarded  Nice Question
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accepted Are there examples of nonconstructive metaproofs?
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comment Are there examples of nonconstructive metaproofs?
Great answer. But I would still be interested in more examples, if anyone has some more.
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awarded  Supporter
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comment Are there examples of nonconstructive metaproofs?
This can hardly be seen as a constructive proof, as the "constructive" part is entirely divorced from the "proof" part.
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comment Are there examples of nonconstructive metaproofs?
Isn't there a story where a famous mathematician was assigned an open problem as homework by a devious professor, and ended up solving it?
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asked Are there examples of nonconstructive metaproofs?
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comment Can Cantor set be the zero set of a continuous function?
Each bump in the bump function has width 1/3^n. If the height is h(n), then the largest value of the kth derivative of of the stage n bumps will be 3^{kn}h(n) times the largest value of the kth derivative of the original bump function. If you want these to converge uniformly, the exact condition you need is that 3^{kn}h(n) converges to 0. So the necessary and sufficient condition on h to make the construction work is that for all a>0, h(n) is eventually less than a^n. So yes, 2^{-2^n} will work.
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accepted Given n k-element subsets of n, is there a small subset A of n which intersects them all?
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comment Given n k-element subsets of n, is there a small subset A of n which intersects them all?
Thank you very much.
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asked Given n k-element subsets of n, is there a small subset A of n which intersects them all?
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accepted Is there a computable model of ZFC?