Day 10: Heart of Mathematics

Last time: Section 3.1 -- one-to-one correspondences

Forget counting; remember one-to-one correspondences.
Is it the end of the world as we know it? Can we throw away elements of a set and not change the size of the set?

Next time: section 3.3: the missing member

Today:

Reminder:
- Project description revision: due today
- Return Homework 2.3 (graded problems #1 and 7)
- Collect Homework 2.4
- Exam 1 is next Monday! The exam will cover through chapter 2. Get ready....
The natural numbers are infinite in number (the size of the set is larger than any natural number).
What is Cardinality?
Two sets have the same cardinality if there is a one-to-one correspondence between them.
A subset is never bigger in size than the set itself.
And if the sets are finite, the proper subset is always smaller....
If the set is infinite, we may actually be able to throw away elements of a set and not change the size of the set!
Let's look at these curious problems (pp. 157):
- 14 - counting cubes
- 16 - Hotel Cardinality
- 17 - Hotel Cardinality (cont.)
- 18 - Hotel Cardinality and the Infinite Life Insurance Co.
The ping-pong ball conundrum

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