Cartesian Product and Induction

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Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

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

Explores the composition of applications in mathematics and the importance of understanding their properties.

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Covers the basics of analysis, including real numbers, proofs, sets, and operations.

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.