Greatest Element is Supremum/Examples/Example 2
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Example of Use of Greatest Element is Supremum
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.
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 2$: Continuum Property: $\S 2.8$: Example $\text{(iii)}$