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.
- Let Tn=(1/n, 1 - 1/n). Find the union ∪ n=2 to infinity of Tn.
(It often helps to draw a picture).
- Let Tn=[-1/n,1 + 1/n]. Find the intersection ∩ n=2 to infinity
- 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.