There are huge differences between zero as the concept of "none" (I had five cows and someone took them all away, how many do I have?), zero as a more formal integer value (e.g. solution to 2 + 7 - 4 + x = 5), zero as unit placeholder (e.g. 101 dalmations), and zero as a real number (on the continuum from positive to negative rationals and irrationals).

When people make claims about "zero" they're essentially meaningless unless they specify which meaning of zero they're talking about.