Bounded Above Subset of Real Numbers/Examples/Open Interval from 3 to Infinity
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Example of Unbounded Above Subset of Real Numbers
Let $I$ be the unbounded open real interval defined as:
- $I := \openint 3 \to$
Then $I$ is not bounded above.
Hence $I$ does not admit a supremum, and so does not have a greatest element.
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 2$: Continuum Property: Exercise $\S 2.10 \ (3) \ \text{(iv)}$