# Writing Intervals to Symbol

It is important to know how to write intervals in symbol. This is basic for some but other people finds it confusing. This is the method that needs to be used to express the solution set of inequalities, expressing the range and domain of an equation, expressing the interval itself, etc. After reading this, you should be able to know how to write different kinds of solution sets in symbol.

Basic Symbols

$\geq$”  read as greater than or equal to

$\leq$”  read as less than or equal to

Parenthesis for Open Intervals

Note: Parenthesis is to emphasize that the start point or endpoint is not included.

{x│x > 1 }  $\to$   ( 1,+∞ )

{x│x < 1 }  $\to$   (-∞ , 1 )

{x│-1 < x < 1 } $\to$  (-1,1)

Bracket for Closed Intervals

Note: Bracket is to emphasize that 1 in included.

{ x│$x \geq 1$ }   $\to$   [ 1, +∞ )

{ x│$x \leq 1$ }    $\to$   ( -∞ , 1]

{ x│$-1\leq x\leq1$ }  $\to$   [-1,1]

Union for Intersection

Union is used to express the intersection of two solution sets

Example 1:

The solution set of $x^2-3x+2>0$ is {x│x>2} or {x│x<1}

To write this in symbol we use unions

{x│x>2} or {x│x<1} can be expressed in symbol as (-∞ , 1 )U(2,+∞ )

Example 2:

The solution set {x│x$\geq$ 2} or {x│x$\leq$ 1} can be expressed in symbols as (-∞ , 1 ]U[2,+∞ )

We will have a separate discussion for this quadratic inequalities.

Writing Set of Real Numbers in Symbol

$\Re$   $\to$     (-∞, +∞ )

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