# "We want the domain of the step function:" \qquad f(x) \ = \ [ 2 x - 1 ]. #
# "1) The linear function," \ 2 x - 1, "is defined for all real numbers," #
# \qquad \quad x. #
# "2) The greatest integer function," \ [ x ], \ "is defined for all real" #
# \qquad \quad "numbers," \ \ x. #
# "3) So now, in language that should be clear:" #
# \qquad \qquad \qquad \qquad f( "real" ) \ = \ [ \ 2("real") -1 \ ] \ = \ [ \ "real" \ ] \ = \ "real". #
# "4) Thus:" #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad f( "real" ) \ = \ "real". #
# \qquad \quad "So:" #
# \qquad \qquad \qquad \qquad \qquad \ f(x) \quad "is defined for all real numbers" \ \ x. #
# \qquad \quad "Thus, in interval notation, and in set notation:" #
# \qquad \qquad \quad \qquad "domain of" \quad f(x) \ = \ ( - infty, infty ) \ = \ RR. #
# "This is our answer." #