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# Infinity

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.

13

120+
1. 1

### Introduction

Tangle with the mathematical idea of the infinite.

1. #### What's Infinite?

What do we really mean when we use the word "infinity"?

2. #### How to Count to Infinity

Reconsider basic counting to handle infinite sets of things.

3. #### Visualizing Infinity

While we can't draw what infinity really looks like, we can make a good attempt!

2. 2

### Sizes of Infinity

Infinity has a "size". How can we compare it with other infinities?

1. Included with

#### Cardinality

Establish one of the basic concepts of set theory.

2. Included with

#### Countably Infinite

Some infinite sets are countable in the same way.

3. Included with

#### Cantor's Quest

Are all infinite sets countable?

4. Included with

#### Hilbert's Infinite Hotel

Help Hilbert use his hotel that has infinitely many rooms to host infinitely many sleepy guests.

3. 3

### Visual Infinities

Represent the infinite in visuals and gain new insights.

1. Included with

#### Infinite Areas

Quantify the infinite using geometry.

2. Included with

#### Infinite Sums

Use infinite area problems to derive the basic ideas behind infinite sums.

3. Included with

#### The Koch Snowflake

Grow this course's first fractal.

4. Included with

#### More Fractals

Making copies of copies of copies of copies of copies of copies...

4. 4

### Hyperbolic Space

Warp space itself to get a new perspective on the infinite.

Coming Soon
5. 5

Coming Soon