Bounded Subset of Real Numbers/Examples/Reciprocals of Positive Integers
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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 $\text{(a)}$