Set Theory (Part 20): The Complex Numbers are Uncountably Infinite

Please feel free to leave comments/questions on the video and practice problems below!

In this video, we will establish a bijection between the complex numbers and the real numbers, showing that the complex numbers are also uncountably infinite. This will eventually mean that the cardinality of the real numbers and the complex numbers are equal, that of the "continuum". We will also show that two bit streams can be combined or multiplexed into a single bitstream in a bijective fashion.

[ostihpem]

This series is just so good, beyond words. It's the only video series that deals with set theory above the usual trivial introduction into the symbolism and basic set algebra while keeping in touch with non-mathematicians. I hope one day it's continued, maybe even enhanced by some mathematical logic.

[ariapratama]

how do you to explain if the complex numbers contain irrational numbers?