Math
Alternating Series Test
Archimedean Property
Bolzano Weismann Theorem
Cauchy Sequences
Fundamental Trigonometric Limit
Limits at Infinity and Asymtotes
Limits of a Function
Limits of a Sequence
Limits of Rational Functions
LUB GLB
Monotone Convergence Theorem (MCT)
Monotonic Sequences
Peak Points
Rational Function
Series
Squeeze Theorem
Subsequence
Tail

Definition
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Every bounded sequence has a convergent Subsequence.

Proof
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Assume that is a bounded sequence. By the Peak Points > Peak Point Lemma, has a Monotonic Sequences (subsequence) . However, is also bounded and therefore converges because of the Monotone Convergence Theorem (MCT)

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Definition

Proof