Week 9:
: The course covers the building blocks of modern math, such as elements, subsets, and set-builder notation. Week 9: : The course covers the building
Problem: Show that √2 is irrational. Low-quality answer: "Assume rational, derive contradiction." Extra Quality answer: Begins with "We use proof by contradiction. Step 1: Write √2 = a/b in lowest terms… Step 2: Square both sides → 2b² = a² → a is even… Step 3: Substitute a=2c → 2b² = 4c² → b² = 2c² → b even. Contradiction (a,b not coprime)." Then adds: Common mistake: forgetting to state "lowest terms" – without that, no contradiction. such as elements