Interval notation

A set in mathematics can be defined as collection of elements. There are different ways in which a set of numbers with end points can be described, roster form, set builder form, interval notation, graphing on a number line and using venn diagrams. Interval notation is a method of representing a set of numbers which describe the span of numbers that lay along an axis namely the x-axis.

An interval can be defined as a subset of the numbers. There are two symbols used in interval notation, an open bracket or parenthesis denotes an open interval in which the number is not included and a square bracket or parenthesis denotes a closed interval in which the number is included.

For instance, (-3,3) is an open interval notation in which both the numbers -3 and 3 are not included in the span of numbers and a closed interval notation is given by [-3,3] where both the numbers -3 and 3 are included in the span of numbers.

For more interval notation practice let us consider the following examples, [-4,1)= {-4, -3,-2,    -1 ,0,1} , this is a half open interval. (-2,1] is a half open interval which is equivalent to set of numbers
 {-1,0,1}.
Let us now learn the steps in solving inequalities in interval notation given the inequality x>-4, here the inequality symbol is greater than but -4 is not included, so it is an open interval and also it is never ending which means it extends till infinity.
So, the interval notation would be (-4,-infinity). Let us now graph and write in interval notation the inequality x<=-2.

In the above graph the closed red dot over -2 shows a closed half interval notation which means -2 is also included in the interval and as the inequality is less than -2 it is towards the left on the number line which shows the other end point is never ending and hence is minus infinity.
Together the half interval notation of the given inequality would be (-infinity, -2]. If there is an open dot over the number on a number line it denotes the number is not included and hence the symbol ‘(‘ or ‘)’. So, inequalities in interval notation are very simple when used with the appropriate parenthesis according to the given inequality.
For instance, 0<=x<6 as="" be="" can="" shown="" x="">-1 would be (-1,+infinity). Absolute value interval notation of |x|< 8 is equivalent to any real number between -8 and 8, the double inequality would be -8