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Least-upper-bound property
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Related lectures (32)
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Bounds and Inequalities
Covers upper and lower bounds, Jensen's inequality, and amended bounds in mathematical analysis.
Lattices for Abstract Interpretation
Covers lattices, abstract interpretation, fixpoint analysis, Hoare logic, and partial orders with extreme elements.
Sequences and Convergence: Understanding Mathematical Foundations
Covers the concepts of sequences, convergence, and boundedness in mathematics.
Math-101(en) / Min/Max, Inf/Sup
Covers minimum, maximum, infimum, and supremum concepts in real numbers with examples and proofs.
Supremum
Covers the concept of supremum in real numbers and its properties as the least upper bound of a set.
Properties of Supremum and Infimum
Covers the properties of supremum and infimum in sets, including uniqueness and symmetry.
Sequences: Convergence and Divergence
Covers convergence, divergence, and the Bolzano-Weierstrass theorem in sequences.
Bisection Algorithm: Convergence and Continuity
Explores the Bisection Algorithm, convergence of sequences, and function continuity.
Real Analysis: Functions and Limits
Covers the basics of real analysis, including functions, limits, and max/min functions.
Infimum and Supremum of Subsets
Covers the concepts of infimum and supremum of subsets in real numbers.
Quiz on Chapters 1-3: Solutions to TF questions
Covers solutions to true/false questions on subsets, upper bounds, real numbers, and set properties.
Sequences and Convergence
Explores sequences, convergence criteria, and accumulation points in sequences.
Inequality in Real Numbers
Explores the equivalence of inequalities to determine the least upper bound of a set.
Bolzano-Weierstrass: Advanced Analysis I
Explores the Bolzano-Weierstrass theorem on bounded sequences and convergent subsequences.
Convergence of Numerical Sequences
Explores the convergence of numerical sequences through monotonicity, boundedness, linear recurrence, and subsequences.
Characterization of Infimum and Supremum
Explores the definitions and properties of infimum and supremum in mathematical analysis.
Real Numbers: Properties and Formulas
Explores real numbers, including supremum, infimum, maximum, and minimum properties.
Real Numbers: Properties and Bounds
Explores real numbers' properties, bounds, limits, and density in the number line.
Cauchy Sequences and Series
Explores Cauchy sequences, convergence, bottoms, and series with illustrative examples.
Analysis I: Convergence and Subsequences
Explores convergence, subsequences, and the Bolzano-Weierstrass theorem in sequences.
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