Plot a single point on number line in interval notation

Question

For example, I want to plot the solution set $\{3\}\cup (2, \infty$). How do I represent 3 as a single point?

Answer 1

The correct notation for a set with only the point $3$ in it is $\{3\}$. If you really want to use interval notation, you could also denote this as $[3,3]$.

Notice that your solution set is just $(2, \infty)$ though, since $3$ is already in the set $(2, \infty)$.

Answer 2

If you needed to represent $\{2\}\cup(4,\infty)$, then you could use a filled-in dot for individual points, so you might draw something like the following:

As Alex G. mentioned, since $3$ is in $(2,\infty)$, $\{3\}\cup(2,\infty)=(2,\infty)$ so you wouldn't have to do this for the case you mentioned in your original question.