Introduction to Analysis: Understanding Real Numbers and Proofs

Related lectures (22)

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Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.

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

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

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

Covers countability and bijections between sets, demonstrating the uncountability of real numbers.

Introduces fundamental concepts of linear algebra, focusing on sets and operations.

Introduces sets in discrete mathematics and explores proof techniques like direct and indirect proofs.

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

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

Covers the fundamental concepts related to real numbers, including sets, notations, and operations.