Distance between Element and Subset of Real Numbers/Examples

Examples of Distances between Elements and Subsets of Real Numbers

Example 1

Let $S \subseteq \R$ be the subset of the set of real numbers $\R$ defined as:

$S := \set {0, 1, 2}$

Then:

$\map d {3, S} = 1$

Example 2

Let $S \subseteq \R$ be the subset of the set of real numbers $\R$ defined as:

$S := \openint 0 1$

Then:

$\map d {3, S} = 1$

Example 3

Let $S \subseteq \R$ be the subset of the set of real numbers $\R$ defined as:

$S := \closedint 1 2$

Then:

$\map d {3, S} = 1$

Example 4

Let $S \subseteq \R$ be the subset of the set of real numbers $\R$ defined as:

$S := \openint 2 3$

Then:

$\map d {3, S} = 0$