Proof
Extension 2 proof techniques covering proof by contradiction, proof by contrapositive, algebraic inequality proofs, and proof by mathematical induction.
Active lessons
4
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
4 of 4 active
Lesson 1
Proof by Contradiction
Assume the negation of a statement, derive a logical or arithmetic contradiction, and identify the conclusion safely through structured proof checkpoints.
Lesson 2
Proof by Contrapositive
Convert P implies Q into not Q implies not P, choose when contrapositive reasoning is efficient, and complete exact parity and divisibility steps.
Lesson 3
Inequalities and Algebraic Proof
Use completing the square, discriminant conditions and non-negative forms to establish inequalities with exact equality conditions.
Lesson 4
Proof by Mathematical Induction
Prove divisibility, inequality and summation statements using strong induction: verify the base case, write a clear inductive hypothesis, and complete the algebraic step that closes the argument.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.