Practice Infinity: Set Theory: Cardinality + Infinity comparation

Practice Infinity

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.

Prerequisites: Measurement

Topics covered: cardinality, subsets, Cantor's theorem, real numbers, fractals, infinite sums, spherical geometry, hyperbolic geometry,

What's Infinite?

1. Introduction Start
   
   1.1 What's Infinite?
   
   1.2 How to Count to Infinity
   
   1.3 Visualizing Infinity

2. Sizes of Infinity
   
   2.1 Cardinality
   
   2.2 Countably Infinite
   
   2.3 Cantor's Quest
   
   2.4 Hilbert's Infinite Hotel
   
   2.5 Subsets
   
   2.6 Cantor's Theorem

3. Visual Infinities
   
   3.1 Infinite Areas
   
   3.2 Infinite Sums
   
   3.3 The Koch Snowflake
   
   3.4 More Fractals

Infinity Counting + Comparation:

https://brilliant.org/courses/infinity/introduction-87/how-to-count-to-infinity/

Cardinality VS Tagging:

Review and Reflect

While it is impossible to count to infinity in the traditional sense of listing numbers in sequence,

we can still “count” and compare infinities by matching objects.

In this course, this will help us discover and prove a number of profound results, such as the existence of infinities that are bigger than others.