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## Main Question or Discussion Point

Does the Archimedean property work for unbounded sets? My book does a proof of the Archimedean property relying on the existence of sup which relies on the existence of a bound.

- Thread starter torquerotates
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- #1

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Does the Archimedean property work for unbounded sets? My book does a proof of the Archimedean property relying on the existence of sup which relies on the existence of a bound.

- #2

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Unbounded sets of what type of elements? Real numbers? I think you should reword or provide more details of your question and maybe even cite the text you're referring to (including page number, theorem number, etc.).Does the Archimedean property work for unbounded sets? My book does a proof of the Archimedean property relying on the existence of sup which relies on the existence of a bound.

- #3

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The real numbers *are* unbounded and have the Archimedean property.

- #4

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I suppose the rational numbers are an example of a set that satisfies the Archimedean property without satisfying the Axiom of Completeness.

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