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

Example of Bounded Below Subset of Real Numbers

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

$I := \openint 3 \to$

Then $I$ is bounded below by, for example, $3$, $2$ and $1$, of which the infimum is $3$.

However, $I$ does not have a smallest element.

Sources

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