Are the calendar months an example of a continuous or discontinuous variable?

Jan 27, 2017

Discontinuous

Explanation:

There are $12$ months in the Gregorian calendar.
Twelve is a counting number.
$12 \in \mathbb{N}$
Since the counting numbers ($\mathbb{N}$) are countable, they deal with the discrete. Discrete is another way of saying not-continuous. Therefore, the calendar months would be a non-continuous random variable.

Any random variable that can only take natural, integer, or rational values is not continuous.

On the other hand if a variable could take values like $e$, $\pi$, or $\sqrt{2}$ then it is continuous