### 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
of Tn.
- 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.