80-110: The Nature of Mathematical Reasoning

Carnegie Mellon University

Spring 2015

Questions about infinity

Due Wednesday, April 8

Think about the following questions before Wednesday's class. You don't need to write up or turn in your answers, but we'll be discussing them: be prepared!

  1. Suppose that S and T are two finite sets. What does it mean to say that S and T have the same number of elements?
  2. What does it mean to say that S and T are finite?
  3. Can you think of an example of a set (either in the language of set theory we showed in class, or just an intuitive "collection" of things) that is infinite? How do you know it's infinite?
  4. Are all infinite sets the same size?