Let X and Y be fixed real numbers such that X < Y on a number line. Various types of intervals as as fallows

1. Open Interval: open interval (x, y) with end points x and y as a set of all real numbers “n”, such that x < n < y. i.e., the real number n will be taking all the values between a and b. An vital point to consider in this case is the type of brackets used. Generally open intervals are denoted by ordinary brackets ( ).

2. The closed interval [x, y]: closed interval [x, y] with end points x and y as a set of all real numbers “n”, such that x <= n <= y. In this case the real number n will be taking all the values between x and y inclusive of the end points x and y. Generally closed intervals are denoted by [ ] brackets.

3. The half open interval [x, y): a half open interval [x, y) with end points x and y as a set of all real numbers “n”, such that x <= n < y. In this case the real number n will be taking all the values between x and y, inclusive of only x but not y. The half open interval in different (x, y].

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