True or False: As a subset of $\bf{R}$: $\emptyset$ has a minimum.
What is the difference between a supremum and the maximum? are they used interchangeably?
2026-04-02 20:54:52.1775163292
Does the empty set have a minimum if it is a subset of R?
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A maximum of a set $A$ is a supremum that is also an element of $A$. But a supremum of $A$ need not be in $A$ necessarily, so all maxima are suprema while not all suprema are maxima.
As an example, the set $[0,1)$ with the standard order on $\mathbb{R}$ has a supremum ($1$) but no maximum.
As for this particular question: it's rather trivial, since a maximum of $A$ is necessarily an element of $A$, but nothing is an element of the empty set.