I see no contradiction to my statement at all: "Zero was introduced to reason about the question of what remains if you have n sheep and give all of them away".

I see no contradiction to my statement at all: "Zero was introduced to reason about the question of what remains if you have n sheep and give all of them away". People invented mathematics to be able to explain things happening in nature, and refined their mathematical devices even further to even explain the nature of mathematics itself. Numbers did not exist before people invented them as sets for different tools to calculate stuff, as you have so eloquently put. To argue that "Real numbers very definitely were not known to humans until the 1700s" means nothing else than these numbers were not invented yet. Um, what is your point exactly?