Greatest Element is Supremum/Examples/Arbitrary Example 2

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 $\text{(iii)}$
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