Logic, Proof and Paradoxes
This topic is about how arguments decide what must be true.
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About this topic
Logic, proof and paradoxes sit close to the foundations of mathematics: what counts as a valid argument, and what happens when intuition breaks.
Use this section to slow thinking down: make a claim, test it, search for a counterexample, then decide what has actually been proved.
Explore this through truth tables and logical connectives, direct proof, contradiction, induction and counterexamples, paradoxes involving infinity, sets and probability.
Further exploration
Look up: proof by contradiction
Explore next: Hilbert's Hotel
Try searching for: truth tables and logical implication