College Math

> ≥ ≤ ≠

is greater than is greater than or equal to is less than or equal to is not equal to

≈ is approximately equal to The symbols <, >, ≥, ≤ and ≠ denote the signs of inequalities and the expressions using these signs of inequalities, < , > , ≥ , ≤ and ≠ denotes inequalities. We can make use of set- builder notation for these inequalities as well. For instance, = { | ≥ 2} means set represents all the values of such that is greater than or equal to 2. This can be shown graphically on the number line as follows: It must be noted that in the above number line, there is a closed bracket [ at 2, which means that 2 is also included in the expression. In contrast, the expression = { | > 2} is represented on the number line as follows: When a parenthesis ( is used on the number line, it means that all numbers greater than 2, excluding 2, are to be considered here. In other words, while using inequalities, we may make use of different types of brackets that have different meanings. For instance, ( , ) means the set contains all the numbers between and , excluding and . On the contrary, [ , ] means all numbers between and , including and . Similarly, [ , ) means all numbers between and , inclusive of and exclusive of . This is known an interval notation . Let us understand this using a few examples: Set-Builder Notation Grap cal Representation Interval Notation { | > 4} (4, ∞)

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