Bounded Subset of Real Numbers/Examples/Reciprocals of Positive Integers

Example of Bounded Subset of Real Numbers
The subset $T$ of the real numbers $\R$ defined as:
 * $T = \set {\dfrac 1 n: n \in \Z_{>0} }$

is bounded both above and below.

We have that:
 * $\sup T = 1$
 * $\inf T = 0$

where $\sup T$ and $\inf T$ denote the supremum and infimum of $T$ respectively.

We also have:
 * $\sup T \in T$
 * $\inf T \notin T$