Earlier quoted context omitted.
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 meaning…
I really wonder how zero came to be, was it a need to homogenize the algebraic tools (we have nice operations and want to reify the 'nothing' dead end into something that can be kept chugging along) or something else /
(mods I promise I'm not here to shill this book but people keep wondering about the history and that's a great resource that I like XD)