How did people count before the invention of the number 0?

You don't need the 0 to count upto any number. The concept of zero is needed to represent "nothing", and the numeral zero is useful for an easy representation of a number. There are many numeral system which doesn't require 0. read more

e.g. the "generalizing" may just as well start at the bottom, not at the top of the number systems - the Babylonians used a number system with a base of 60. They expressed all numbers smaller than 60 with just two symbols, one for tens and one for units. read more

Well technically, it's impossible to give 0 fucks without the invention of 0. However, people at the time really did'nt give a fuck, and simply did as they pleased without considering that. read more