Back to all courses

Infinity

Expand your mind with the paradoxes and beauties of 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.

Interactive
quizzes

13

Concepts and
exercises

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
      Brilliant Premium

      Cardinality

      Establish one of the basic concepts of set theory.

    2. Included with
      Brilliant Premium

      Countably Infinite

      Some infinite sets are countable in the same way.

    3. Included with
      Brilliant Premium

      Cantor's Quest

      Are all infinite sets countable?

    4. Included with
      Brilliant Premium

      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
      Brilliant Premium

      Infinite Areas

      Quantify the infinite using geometry.

    2. Included with
      Brilliant Premium

      Infinite Sums

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

    3. Included with
      Brilliant Premium

      The Koch Snowflake

      Grow this course's first fractal.

    4. Included with
      Brilliant Premium

      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

    0.999...=1

    Coming Soon
骚虎高清影音-骚虎高清-骚虎高清官方