In part two of his “Probabilities of probabilities” series, 3Blue1Brown explains why a probability of zero does not imply impossibility, delving into probability density functions and the subtleties of measure theory. He references Terence Tao’s real‑analysis text for deeper background, and poses a puzzle: if every value in a real‑number range has a non‑zero probability, no matter how tiny, the sum of those probabilities must diverge to infinity, illustrating how uncountable collections of positive numbers behave. The video also encourages viewers to support future projects, mentions the music by Vincent Rubinetti, and thanks contributors for translations.
Key topics
- Probability density function — A function that describes the likelihood of a continuous random variable taking on a specific value.
- Measure theory — A branch of mathematics that formalizes the concept of size or probability for sets, underpinning continuous probability.