[mgsouth]

Haven't seen the paper, but I'd guess the argument is something like "if the domain for x includes 0, then [edit: whenever x = 0] the Turing machine will get into an infinite loop looking for the first inverted bit[1]. _None_ of the three states will ever be provably true or false. If the domain _excludes_ 0 then you can prove that the machine will hit a non-zero bit in finite time, thus terminate, and either x<0 or x>0 will be shown true. But if you exclude 0 then you've also shown that the =0 state will never be true."

[1] multiple zero bits and a one bit is >0, multiple 1 bits and a zero bit is <0. Infinite zero bits (even if followed by a one bit) is +0, infinite 1 bits (even if followed by a zero bit) is -0.