Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2

An introduction to probability density functions Home page: Brought to you by you: Curious about measure theory? This does require some background in real analysis, but if you want to dig in, here is a textbook by the always great Terence Tao. Also, for the real analysis buffs among you, there was one statement I made in this video that is a rather nice puzzle. Namely, if the probabilities for each value in a given range (of the real number line) are all non-zero, no matter how small, their sum will be infinite. This isn’t immediately obvious, given that you can have convergent sums of countable infinitely many values, but if you’re up for it see if you can prove that the sum of any uncountable infinite collection of positive values must blow up to infinity. ------------------ These animations are largely made using manim, a scrappy open source python library: