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Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

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

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

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

Covers simplicial and cosimplicial objects in category theory with practical examples.

Covers abbreviated calculation, structures, operations, and unique set properties.