Consider the function defined on .

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions

Problem

Consider the function

s(x)=\operatorname{sgn}(x)

defined on

\mathbb R

. (i) State the algebraic definition of

\operatorname{sgn}(x)

for all real values of

x

. (ii) Using the definition, list the complete set of values that

s(x)

can assume and justify your answer. (iii) Explain why the range obtained in part (ii) is called a discrete set rather than an interval.