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Gaussian rational
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Real Numbers: Structure and Properties
Covers the structure and properties of real numbers, including the introduction to the axiomatic system and the implications of Archimedean property.
Continuity of a Function
Explores the conditions for continuity of a function on real numbers.
Introduction to Analysis: Understanding Real Numbers and Proofs
Covers the basics of analysis, including real numbers, proofs, sets, and operations.
Real Numbers: Properties and Formulas
Explores real numbers, including supremum, infimum, maximum, and minimum properties.
Decimal and Periodic Numbers
Explains decimal and periodic numbers, illustrating with examples and discussing rational numbers.
Infimum and Supremum of Subsets
Covers the concepts of infimum and supremum of subsets in real numbers.
Rational Numbers: Construction and Properties
Covers the construction and properties of rational numbers, including fractions and equivalence, with proofs on commutativity.
Real Analysis: Basics and Sequences
Introduces real analysis basics, including functions, sequences, limits, and set properties in R.
Infimum and Supremum: Understanding Bounded Sets
Explains infimum, supremum, Archimedes' properties, rational numbers density, and exercises on irrational numbers and minimum values.
Boundary Analysis
Explores boundaries in sets, defining them as points not well separated from the set or its complement.