hw2 - MATH 444 ELEMENTARY REAL ANALYSIS HOMEWORK 2 Due on...

Info icon This preview shows page 1. Sign up to view the full content.

MATH 444: ELEMENTARY REAL ANALYSIS HOMEWORK 2 Due on Wednesday, Sep 10 Exercises from the textbook. 1.3: 12 2.2: 16; 17 Out-of-textbook exercises (these are as mandatory as the ones from the textbook) . 1. (a) Let n N and prove that every subset A of { 1 , 2 , ..., n } is finite. Hint : Prove this by induction on n . For the step of induction, let A be a subset of { 1 , 2 , ..., n, n + 1 } and note that B := A \ { n + 1 } is a subset of { 1 , 2 , ..., n } . (b) Conclude from part (a) that any subset of a finite set is finite. 2. Prove that if a set A is denumerable then there is a proper subset B A such that B A , i.e. there is a bijection between
Image of page 1
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