Mathematics
Structure, proof, and surprising consequences.
Mathematics
Why does 0.999... equal exactly 1?
Because the notation does not mean a number creeping toward one — it means the value the sequence of finite pieces converges to, and that value is exactly one.
6 min readintermediate1
Mathematics
Why do 23 people give a 50% chance of a shared birthday?
Because you are not comparing 23 birthdays against 365 days — you are comparing 253 pairs of people against each other, and 253 chances at a 1-in-365 event is a coin flip.
6 min readintermediate
Mathematics
Why can't you divide by zero?
Division asks what you must multiply by to get back where you started, and multiplying by zero destroys that information — so the question either has no answer or has every answer.
5 min read