Foundations · Module 01
Every later module assumes you can do this. It is the one thing school mathematics almost never teaches, and the one thing university mathematics assumes on day one.
By the end of this module
You can read and write a proof, and tell a real argument from a plausible one.
Why is 'it works for the first thousand cases' not enough?
Richard Hammack, VCU
Free, complete, and the friendliest entry into rigour that exists.
3Blue1Brown
Why intuition needs proof: the answer is π, and nothing about the setup suggests it.
What does 'if...then' actually commit me to?
MIT OCW
Tom Leighton. Logic, proof and discrete structures, taught superbly.
Are some infinities bigger than others?
How can a finite argument establish infinitely many facts?
Check yourself
Every answer comes with the reasoning, not just a verdict. Getting one wrong and reading why is the point.
01The statement 'if it rains, the ground is wet' is FALSE only when:
02Cantor's diagonal argument shows that:
03Proof by contradiction works because: