Set Theory Exercises 1

  • Write up the following and be sure to give proper reference and credit where it is due. You may work alone or in a group of up to 3 people and turn in 1 per group. Make copies of your work so that you are prepared to present any of the exercises after you turn it in.
    1. Let Tn=(1/n, 1 - 1/n). Find the union ∪ n=2 to infinity of Tn. (It often helps to draw a picture).
    2. Let Tn=[-1/n,1 + 1/n]. Find the intersection ∩ n=2 to infinity of Tn.
    3. Research and write out a proof of the intermediate value theorem in your own words.

    Problem for Graduate Students No path can be found between the seven Konigsberg (now Kaliningrad, in Russia) bridges, since this is exactly what Euler proved. Search on the web or in a library, find useful references, and summarize why no such path can be found.