# 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!

- 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?
- What does it mean to say that S and T are finite?
- 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?
- Are all infinite sets the same size?