Mathematics

Problem

Which of the following sets is the range of

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

for all real

x

? a)

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

\mathbb{Z}

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

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