Bounded Above Subset of Real Numbers/Examples/Open Interval from 3 to Infinity

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 $\S 2.10 \ (3) \ \text{(iv)}$