Recent content by rbzima

Figured it out... Thanks for the help... Essentially, gcd(k, k+1) is a good candidate! =)

Homework Statement We select n + 1 different integers from the set {1,2,...,2n}. Prove that there will always be two among the selected integers whose largest common divisor is 1. Homework Equations None The Attempt at a Solution I was thinking that this problem has something to...

Wow, long night... http://scienceblogs.com/insolence/facepalm.jpg [/URL]

Homework Statement Prove that \left(ab+cd\right)^{2} \leq \left(a^{2}+c^{2}\right)\left(b^{2}+d^{2}\right) Homework Equations None The Attempt at a Solution I've broken the LHS down to the following: \left(ab\right)^{2}+2abcd+\left(cd\right)^{2} The RHS...

Any reason why you want to use it? Are you attempting to vizualize a vertical line test. Just go to 2nd, draw, vertical... It should show up on the home screen, then just input x=9. Hope that helps.

Homework Statement One afternoon, a mathematics library had several visitors. A librarian noticed that it was impossible to find three visitors so that no two of them met in the library that afternoon. Prove that then it was possible to find two moments of time that afternoon so that each...

Wow, that was straight forward... Totally figured it out... I had an epiphany right before you responded, so I should be good now. I was definitely thinking the same thing, and ended up solving in terms of a_{1}. Regardless of how small a_{1} is, as long as it's not 0, you will receive some...

Homework Statement The sum of 5 positive real numbers is 100. Prove that there are two numbers among them whose difference is at most 10. Homework Equations Nothing really... The Attempt at a Solution The biggest problem I'm running into is that I can think of specific examples...

|x_n - y_n| need to converge to 0. |f(x_n ) - f(y_n)| needs to converge to some real number, where f(x) = x^3

I'm trying to show a function has non-uniform continuity, and I can't seem to think of 2 sequences (xn) and (yn) where |(xn) - (yn)| approaches zero, where f(x) = x3. Can anyone think of two sequences?

Hey guys, I'm in a little bit of a jam here: I managed to miss a really important lecture on continuity the other day, and there were a few examples that the professor provided to the class that I just got, but would love it if someone could explain them to me. First, f(x)=x3 is continuous...

This is for a general Real Analysis course at my college. We are a relatively small college that doesn't offer many variations of Analysis, just the basics. Thanks for the help though. I feel a little behind because I missed a day last week, but we'll see how things go.

This is review from class the other day that I managed to miss because of illness and I was wondering if someone could explain how to go about solving these problems: #1 Let B = \left\{ \frac{(-1)^nn}{n+1}:n = 1,2,3,...\right\} Find the limit points of B Is B a closed set? Is B an open set...

Wow, ok nevermind: We know \sum x_n converges. |yn| <= M, For any n contained in the naturals - Def of bounded. Then, \sum x_n y_n = \sum \left|x_n\right| \left|y_n\right| \leq M\sum \left|x_n\right| Therefore, the sum converges! A counter example would be to let xn =...

I'm not entirely sure I follow you... Are you suggesting I choose lim(sup{xn}) or lim(inf{xn}, which are both monotone decreasing and increasing respectively?