1. Infinity and Beyond!
A prelude to Infinite Sequences and Series (Chps 9-10)

3. Infinity and Fractals…
Fractals are self-similar objects whose overall geometric form and structure repeat at various scales they provide us with a “glimpse” into the wonderful way in which nature and mathematics meet.
Fractals often arise when investigating numerical solutions of differential (and other equations).
… go to XAOS

4. Paradoxes of Infinity Zeno Motion is impossible
Achilles and the tortoise
Math prof version

5. Sizes of Infinity… How can you decide if two sets are the same size?
How many fractions are there between 0 and 1?
Which is bigger – the set of counting numbers or the et of fractions?

6. Cantor (and the concept of countable and uncountable sets)
In the 1870’s Cantor began his great work on the theory of sets and in so doing startled the mathematical world with fundamental discoveries concerning the nature of infinity.
Cantor developed the idea of countable and uncountable sets…

7. Why the number of Rationals is the same as the number of Naturals

8. What about the “number” of irrationals?

9. We can always make a number that is not on the listed on enumerated reals! The reals are uncountable!