Proofs by Induction: Principles and Examples

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Related lectures (27)

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Recurrence: Induction

Covers the principle of induction for natural numbers and the importance of caution in its application.

Recursion and Induction: Understanding Mathematical Proofs

Explores recursion and induction for mathematical proofs through recursive algorithms and functions.

Mathematical Recursion: Induction and Recursion

Explains mathematical induction for proving propositions true for all positive integers.

Mathematical Induction: Principle and Example MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Introduces the principle of mathematical induction through an example.

Mathematical Recursion: Induction and Recursion

Covers the principle of mathematical induction for proving propositions true for all positive integers.

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Recurrence Demonstrations: Principle and Examples

Covers the principle of recurrence demonstrations with examples illustrating the process step by step.

Geometric Series: Convergence and Applications

Explores the convergence of geometric series and their applications in real-world problems.

Complexity & Induction: Algorithms & Proofs

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

Complexity & Induction: Algorithms & Proofs

Explores worst-case complexity, mathematical induction, and algorithms like binary search and insertion sort.

Strong Induction: The Power of Mathematical Proof

Explores strong induction as a powerful proof method with advantages over mathematical induction, demonstrated through a theorem about expressing integers as sums of powers of two.

Mathematical Induction: Basics and Applications

Introduces mathematical induction principles and applications, including inequalities, divisibility, subsets, and strong induction.

Induction and Recursion: Examples + Q&A

Covers examples and a Q&A session on induction and recursion.

Linear Algebra: Propositions and Sets

Covers propositions indexed by vectors, proof by induction, and Cartesian products of sets.

Strong Induction: Proof Method and Application

Explores strong induction as a proof method and demonstrates its application in proving a theorem about positive integers.

Recursively Defined Functions

Introduces recursively defined functions and demonstrates how to compute values and prove properties using mathematical induction.

Modular Arithmetic: Foundations and Applications

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Supremum Theorem

Explores the Supremum Theorem, its properties, proofs, and exercises.

Mathematical Induction: Proofs and Subsets

Covers proofs by mathematical induction and the number of subsets of a finite set.

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