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bio website gpfreitas.net
location United States
age 32
visits member for 2 years
seen Nov 20 '13 at 2:00

Mathematical Economist by training (Caltech, IMPA, UnB) and hobbyist programmer with a strong interest in Optimization/Mathematical Programming and a range of applied problems.


Nov
6
awarded  Supporter
Oct
23
answered More Theoretical and Less Computational Linear Algebra Textbook
Oct
23
comment Show that a function that is locally increasing is increasing?
Adding to coffeemath's point: remember the property (maybe definition, depends how you go about it) of compact sets in $\mathbb{R}$ that "every open covering has a finite subcovering". That should allow you to "globalize" the local statement.
Oct
23
revised Comparison of nonlinear system solvers?
Expand on the previous answer.
Oct
23
revised Question regarding Kuhn-Tucker multiplier
added 361 characters in body
Oct
23
revised Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space?
Clarify where the supplied "proof" fails, based on the comments.
Oct
23
revised Question regarding Kuhn-Tucker multiplier
Cleanup. I cannot understand what is being asked in item (c).
Oct
23
answered Question regarding Kuhn-Tucker multiplier
Oct
23
suggested suggested edit on Question regarding Kuhn-Tucker multiplier
Oct
23
revised Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space?
THERE WAS A MISTAKE IN THE PROOF. Giving proper credit in the main post.
Oct
23
comment Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space?
Agreed. Bit by the "yeah... this should be obvious". My mistake was when I wrote "and more importantly, that $\lim z_{m} = 0$", because, for example the numbers $d(h(y_{m+p}), h(y_{m})$ may be constant (for all positive integers $p$). Counterexamples have already been mentioned (thanks, Asaf, Nate). More explicitly: in my setup, if $Y = (-1, 1)$, $X = \mathbb{R}$ and $h^{-1}(x) = \frac{x}{1+|x|}$, then setting $x_{n} = n$ and $y_{n} = h^{-1}(x_{n})$, we obtain $y_n$ that increases monotonically towards 1, and is thus Cauchy. But $x_{n}$ is not Cauchy, by construction. Thanks, guys.
Oct
23
comment Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space?
Sorry, I didn't know about the 5min to comment rule. I'll reply shortly.
Oct
23
comment Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space?
> Homeomorphism is not necessarily an isometry.
Oct
23
awarded  Revival
Oct
23
awarded  Editor
Oct
23
revised Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space?
Giving some intuition before the proof.
Oct
23
answered Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space?
Oct
23
awarded  Teacher
Oct
23
answered Are the Karush-Kuhn-Tucker conditions applicable when one or more of the constraints are nonlinear?
Oct
23
answered Comparison of nonlinear system solvers?