{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

204ps22006 - Economics 204 August 2006 Due Tuesday 8 August...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Problem Set 2 Economics 204 - August 2006 Due Tuesday, 8 August in Lecture 1. Theorem 4 from the lim inf/lim sup handout: Let { x n } be a sequence of real numbers. Then lim x →∞ x n = x R ∪ {-∞ , ∞} if and only if lim inf x →∞ x n = lim sup x →∞ x n = x. Prove this theorem for the case that x is finite. 2. Using the definition of an open set, prove that (0 , 1) is an open subset of R (a) Under the usual absolute value metric. (b) Under the discrete metric. 3. Construct a sequence of real numbers (a) That is unbounded and has exactly three cluster points. (b) That is bounded and has infinitely many cluster points. 4. Prove that lim n →∞ ( n 2 + n - n ) = 1 / 2. 5. Closure, Boundary, Interior, etc. (a) Let A , B , denote subsets of a space X . Determine whether the following equations hold; if an equality fails, determine whether one of the inclusions or holds. 1. cl( A B ) = cl A cl B . 2. cl( A \ B ) = cl A \ cl B . (b) Find the boundary and the interior of each of the following subsets of R 2 : 1. A = { ( x, y ) | y = 0 } 2. B = { ( x, y ) | x > 0 and y = 0 } 3. C = A
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern