## Infinity

Expand your mind with the paradoxes and beauties of infinity.

What's Infinite?

How to Count to Infinity

Visualizing Infinity

Cardinality

Countably Infinite

Cantor's Quest

Hilbert's Infinite Hotel

Subsets

Cantor's Theorem

Infinite Areas

Infinite Sums

The Koch Snowflake

More Fractals

### Course description

Reckoning with infinity is one of the major accomplishments of mathematics. Start with basic counting and work your way up to the many types of infinity, culminating in the profundity of Cantor's theorem. Explore the stunning beauty of fractals, where it's turtles all the way down, and tesselations in hyperbolic space, where the infinitely large is bounded by a simple circle.

### Topics covered

- cardinality
- subsets
- Cantor's theorem
- real numbers
- fractals
- infinite sums
- spherical geometry
- hyperbolic geometry