Order of Real Numbers
Let and be two real numbers. Then
is less than , written if is to the left of .
is less than , written if is to the right of .
Variations of and :
-- less than or equal to
-- greater than or equal to
-- not less than
-- not greater than
An inequality is a statement involving symbols , , , , , , , .
Ex. , ,
The inequality says that is between and .
Absolute Values of Real Numbers
The absolute value of a real number is the distance from the number to 0 on the number line. The absolute value of is written as . For all real numbers
Properties of absolute values For all real numbers and :
5. (triangle inequality)
Distance between two points on a number line
Let P and Q be two points on the number line with coordinates and respectively. Then
the distance between and is