80-110   The Nature of Mathematical Reasoning

Spring 2001

Dirk Schlimm

Homework No. 12

Thursday, April 19, 2001
Due Tuesday, April 24, 2001

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:

  1. Page 220, Problem 26. (5 extra points)