Which of the following sets is the range of for all real ?

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

Which of the following sets is the range of

h(x)=\lfloor x\rfloor\,\operatorname{sgn}(x)

for all real

x

? (a)

\{1,2,3,\dots\}

(b)

\mathbb{Z}

(c)

\{0,1,2,3,\dots\}

(d)

\{0,-1,-2,\dots\}