Examples on Analysis

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SETS AND NUMBERS

• Logic and proof
• Sets and their operations
• Relations and functions
• Basic properties of functions
• Cardinality

• Numbers
• Completeness
• Topology of R
• Compactness

• Sequences
• Convergence
• Limit superior and limit inferior

• Limit of functions
• Continuity
• Uniform continuity
• The derivative
• The Riemann integral

• Infinite series
• Sequences and series of functions