Bounded Below Subset of Real Numbers/Examples/Open Interval from 0 to Infinity

Example of Bounded Below Subset of Real Numbers
The subset $T$ of the real numbers $\R$ defined as:
 * $T = \set {x \in \R: x > 0}$

is bounded below, but unbounded above.

Let $H > 0$ in $T$ be proposed as an upper bound.

Then it is seen that $H + 1 \in T$ and so $H$ is not an upper bound at all.

Examples of lower bounds of $T$ are:
 * $-27, 0$

Its infimum is $0$.