How to Prove a Number is Irrational

In this episode, I'll show you some surprisingly simple proofs that certain numbers (like the square root of 2) are “irrational”, and explain what has been proven about other numbers like pi, e, and “Legendre’s constant”. Timestamps of different chapters:
0:00 - Introduction
1:50 - Proving a Logarithm is Irrational
3:50 - Proving a Square Root is Irrational
9:26 - What About Pi and E?
11:36 - The Funny Tale of Legendre’s Constant
15:13 - Conclusion

Some previous episodes I mentioned in this one:

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This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.

Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.