Home page for accesible maths Math 101 Chapter 2: Functions of a real variable

Style control - access keys in brackets

Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

2.16 The modulus functions

The modulus function is

|x|=x,  x0;|x|=x,\qquad x\geq 0;
|x|=-x,  x<0.|x|=-x,\qquad x<0.

Note that |x|0|x|\geq 0 for any real xx, and -|x|x|x|.-|x|\leq x\leq|x|. Some computers use the term absolute function or abs(x){\hbox{abs}}(x) for the modulus function. The idea is that |x||x| measures the absolute size of the real number xx, and that |x-y||x-y| measures the distance between points xx and yy on the real line.

Example

Is the modulus function continuous?