Guilherme Freitas

66 reputation

bio	website	gpfreitas.net
	location	United States
	age	30
visits	member for	7 months
	seen	Dec 11 '12 at 23:52
stats	profile views	22

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

	66 reputation	bio	website	gpfreitas.net	visits	member for	7 months
5 badges		location	United States		seen	Dec 11 '12 at 23:52

summary answers questions tags badges favorites bounties reputation activity

21 Actions

suggestions reviews revisions comments badges posts accepts all

Nov 6	awarded	Supporter
Oct 23	answered	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?