Bounded Above Subset of Real Numbers/Examples/Closed Interval from Minus Infinity to 2

Example of Bounded Above Subset of Real Numbers

The subset $I$ of the real numbers $\R$ defined as:

$I = \hointl \gets 2$

is bounded above by, for example, $2$, $3$ and $4$, of which the supremum is $2$.

$2$ is also the greatest element of $I$.

The set of all upper bounds of $I$ is:

$\closedint 2 \to$

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 10$: The well-ordering principle
• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 2$: Continuum Property: Exercise $\S 2.10 \ (3) \ \text{(ii)}$