Mathematical Proofs: Induction, Inequalities, Divisibility, Subsets

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Cartesian Product and Induction

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

Mathematical Induction: Proofs and Subsets

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

Proofs: Logic, Mathematics & Algorithms

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

Formal Logic: Proofs and Sets

Covers the basics of formal logic, focusing on logical expressions and mathematical proofs.

Proofs by Induction: Principles and Examples

Explains the induction principle and proofs by induction with examples like 1 + 3 + 5 + ... + (2n-1) = n².

Recursively Defined Functions

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

Fourier Inversion Formula

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

Recursion and Induction: Understanding Mathematical Proofs

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

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.

Existence of Gibbs measures

Explores quasilocality in statistical mechanics and the existence conditions of Gibbs measures.