Analysis: Chapter 4 Real numbers

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Definition of upper and lower bounds.

Definition of bounded above, below and just bounded.

Definition of least upper bound.

Definition of supremum.

Axiom of completeness…

Definition of infimum.

Alternative characterization of supremum.

Alternative characterization of infimum.

Definition of maximum and minimum.

Three propositions around minimum and maximum.

Archimedean property…

(Archimedean property). For every real number x ∈ R there exists a natural number m ∈N such that x < m.

Definition of a ceiling function.

Proposition & properties of infimum and supremum.

Definition of Bernoulli’s inequality