Analysis: Chapter 14 Real-valued functions

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Theorem - Limit laws for real-valued functions

Theorem - translating limits laws to statements about continuity

Continuity for polynomials

Continuity for rational functions

Continuity of some standard functions

Definition - limit from the left

Definition - limit from the right

Definition - the extended real line

Definition - distance of the extended real line

Definition - divergence to infinity

Definition - divergence to negative infinity

Alternative characterization of divergence to ∞

As x goes to infinity (limit)

Unbounded below

Divergence to and at infinity

Divergence to and at infinity

Limit table 1

Limit table 2

Theorem - IVT

Theorem - EVT

Definition - Equivalent norms

Theorem- Equivalence of norms on finite-dimensional vector spaces

Theorem - complete finite dim normed vector space

Heine-Borel Theorem for finite-dimensional normed vector spaces

Definition - linear map

Definition - bounded linear map

Proposition - bounded linear map

Alternative characterization of boundedness of linear maps

Proposition - 2 normed vector spaces

Definition - operator norm

Proposition - normed vector spaces

Theorem - normed vector spaces and a map

Theorem - normed vector spaces and a continuous map