Bounded Below Subset of Real Numbers/Examples/Closed Interval from Minus Infinity to 2

Example of Bounded Below Subset of Real Numbers

Let $I$ be the open real interval defined as:

$I := \openint 0 1$

Then $I$ is not bounded below.

Hence $I$ does not admit an infimum, and so does not have a smallest element.

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 2$: Continuum Property: Exercise $\S 2.10 \ (4) \ \text{(ii)}$