Analysis: Chapter 6 Real-valued sequences

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Increasing and decreasing monotone sequences.

Upper bound and lower bound for a sequence.

Bounded above and below for a sequence.

Theorem on monotone convergent sequences.

Theorem of the infimum and limit of a sequence.

Limits theorems for real valued sequences.

The squeeze theorem.

Divergence to ∞ and−∞

Proposition on infinities and sequences.

Theorem on properties of sequences and infinities.

Proposition

Proposition on the standard limit of geometric sequences.

Limit of the nth root of n

Lemma on an increasing sequence

Another lemma on the e sequence.

Definition of e via the limit

Exponentials beat powers

Proposition on sequences with values in R^d