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:

\(\ds \sup T\)

\(=\)

\(\ds 1\)

\(\ds \inf T\)

\(=\)

\(\ds 0\)

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

We also have:

\(\ds \sup T\)

\(\in\)

\(\ds T\)

\(\ds \inf T\)

\(\notin\)

\(\ds T\)

Sources

• 1964: Walter Rudin: Principles of Mathematical Analysis (2nd ed.) ... (previous) ... (next): Chapter $1$: The Real and Complex Number Systems: Real Numbers: $1.35$. Example $\text{(a)}$