documentclass[11pt]{amsart}
usepackage{mathtools}
usepackage{enumitem}
DeclarePairedDelimiterfloor{lfloor}{rfloor} % floor function fences
begin{document}
Prove that the greatest-integer function, $floor{x}$, has the properties indicated.
begin{enumerate}[label=(alph*)]
    item $floor{x + n} = floor{x} + n,$ for every integer $n$.
    item [
        floor{-x} = begin{cases}
            - floor{x} & text{if } x text{ is an integer}, \
            - floor{x} -1 & text{otherwise.}
        end{cases}
        ]
    item $floor{x+y} = floor{x} + floor{y} qquad text{or} qquad floor{x} + floor{y} +1$.
    item $floor{2x} = floor{x} + floor{x + frac{1}{2}}$
    item $floor{3x} = floor{x} + floor{x + frac{1}{3}} + floor{x + frac{1}{3}}$
end{enumerate}
end{document}