Bounded Above Subset of Real Numbers/Examples/Real Numbers
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Example of Unbounded Above Subset of Real Numbers
Let $\R$ denote the set of real numbers.
$\R$ is not bounded above.
Proof
Follows directly from the Axiom of Archimedes.
$\blacksquare$
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $1$: Review of some real analysis: $\S 1.1$: Real Numbers: Example $1.1.1 \ \text{(a)}$