Dirk Schlimm
1. 1-1 Functions. (2 points)
Take a set A={alligator, bear, chimpanzee} and a set B={apple, banana,
cherry}. Write down two functions from A to B, one of which is 1-1 and
one which is not.
2. Cardinality.
(4 points)
Prove: The cardinality of the even numbers is the same as the
cardinality of the natural numbers.
3. The Non-Denumerability of the
Continuum. (4 points)
Read Handouts #23 and #24.
(Optional). Set theory.
If you are
interested to know more about Russell's Paradox and modern set theory,
read FOL, pages 216-224 (Sections
8.5-8.8). Attempt the following problem: