Greatest Element is Supremum/Examples
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Examples of Use of Greatest Element is Supremum
Example 1
Let $S$ be the subset of the real numbers $\R$ defined as:
- $S = \set {1, 2, 3}$
Then the greatest element of $S$ is $3$.
From Greatest Element is Supremum it follows that:
- $\sup S = 3$
Example 2
Let $V$ be the subset of the real numbers $\R$ defined as:
- $V := \set {x \in \R: x > 0}$
From Supremum of Subset of Real Numbers: Example 3, $V$ has no supremum.
It follows from Greatest Element is Supremum that $V$ has no greatest element either.