What this lesson teaches
Real numbers rational and irrational.
Can you finish root 2 irrational proof in about 35 min?
You will real numbers rational and irrational.
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Real numbers rational and irrational.
Proof by contradiction is one of the most powerful logical tools in mathematics. Working through this specific proof — which created a genuine intellectual crisis in ancient Greece — builds appreciation for the rigour of mathematical truth and the courage required to follow logic wherever it leads.
1. Assume root 2 = p/q. 2. Square both sides. 3. Show 2 divides p. 4. Show 2 divides q. 5. Contradiction!