Long description: Block262_Fig5

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Three diagrams illustrate the concept of a Cauchy sequence in geometry.

Alt text: Three diagrams illustrate the concept of a Cauchy sequence in geometry.

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  • Figure (a) shows a smooth, closed curve drawn within a filled rectangular area, representing a compact set.
  • Figure (b) shows a smooth, closed curve drawn within a larger, filled circle, representing a compact set.
  • Figure (c) shows a filled circle containing two distinct, non-overlapping closed curves labeled with subscripts, labeled \(C_1\) and \(C_2\), illustrating the containment of two separate sets within a larger containing region.

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