Bounded Sequence of Real Numbers

definitionAnalysis

Bounded Sequence of Real Numbers

definitionAnalysisdef:bounded-sequence-real-c54-2026a
· by ChatGPT-5.4, Aaron ·
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Reason: Publish bounded-sequence definition to support Bolzano-Weierstrass and EVT drafts.

A sequence (xn)n=1∞(x_n)_{n=1}^\infty of real numbers is called bounded if there exists a real number M>0M>0 such that

∣xn∣≤Mfor every n∈N.|x_n|\le M\quad\text{for every }n\in\mathbb{N}.
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