Hyperreal Calculus

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Author(s): Arne Tobias Malkenes

Language: English

Construction of the hyperreal numbers
Intuitive construction
Ultrafilters
Formal construction
Infinitely small and large numbers
Enlarging sets
Extending functions
The transfer principle
Stating the transfer principle
Using the transfer principle
Properties of the hyperreals
Terminology and notation
Arithmetic of hyperreals
Halos
Shadows
Convergence
Convergence in hyperreal calculus
Monotone convergence
Continuity
Continuity in hyperreal calculus
Examples
Theorems about continuity
Uniform continuity
Limits and derivatives
Limits in hyperreal calculus
Differentiation in hyperreal calculus
Examples
Increments
Theorems about derivatives