Infimum and Supremum: Understanding Bounded Sets

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Page 3 of 4

Supremum

Covers the concept of supremum in real numbers and its properties as the least upper bound of a set.

Real Numbers: Definitions and Bounds

Explains the definitions and properties of maximum, minimum, supremum, and infimum in real numbers.

Intervals: Real Numbers

Explores intervals in real numbers, including open and closed intervals, periodic decimals, and irrational numbers.

Exemple: Infimum and Supremum

Illustrates the calculation of infimum and supremum for a set of elements.

Real Numbers: Definitions and Equivalence Classes

Covers the existence of real numbers and equivalence classes of Cauchy sequences.

Quiz on Chapters 1-3: Solutions to TF questions

Covers solutions to true/false questions on subsets, upper bounds, real numbers, and set properties.

Decimal Development

Delves into infinite decimal numbers, exploring convergence and divergence, and showcasing examples of rational and irrational numbers.

Bolzano-Weierstrass: Advanced Analysis I

Explores the Bolzano-Weierstrass theorem on bounded sequences and convergent subsequences.

Convergence of Monotonic Sequences

Covers the convergence of monotonic sequences, discussing how a monotonically increasing or decreasing sequence that is bounded converges to its supremum or infimum respectively.

Convergence of Numerical Sequences

Explores the convergence of numerical sequences through monotonicity, boundedness, linear recurrence, and subsequences.