For instance, an interval could be finite on both sides (closed interval) or it is finite on the left side and infinite to the right side, or it is finite on the right side and infinite to the left side.

Why?

The ends of an interval given by finite numbers are creating finite intervals. The ends represented by the infinite symbol, that is not a value, create the infinite interval.

An interval could have both ends infinite (and it represents the real set number R), both ends finite (finite interval), or one end finite and the other infinite.

(-infinite ; infinite) - R set number(5,6) - finite opened interval

[-1,60) - finite interval, closed to the left and opened to the right

(-10,0] - finite interval, closed to the right and opened to the left

[1,2] - finite closed interval

(6,+infinite) - finite on the left side and infinite to the right side