Terms
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Term
Definition 2.2.3 (Convergence of a Sequence)
Definition
A sequence (an) converges to a real number a if, for every positive number epsilon, there exists N in the natural numbers such that whenever n>=N it follows that |an-a|<epsilon
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Definition 2.3.1 (Bounded Sequence)
Definition
A sequence (xn) is bounded if there exists a number M>0 such that |xn|<=M for all n in the natural numbers
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Theorem 2.3.2
Definition
Every convergent sequence is bounded
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