There are mathematical constructs which do not involve the concept known as zero. It will surprise many people who haven't taken university level mathematics but numbers are not the fundamental foundation of mathematics. There are entire mathematical constructs where numbers are not considered but instead other logical constructs are considered. Once again an assertion of yours, one which you think is in no doubt, is demonstrably false. A simple example is category theory. Yes, particular categories will pertain to numbers but the abstract concept of a category, in the mathematical meaning of the word, has no requirement for the concept of zero. There, a demonstrably false assertion from you becomes a demonstrated false assertion from you. Want another example? You say 'greater than zero'. There are mathematical constructs where 'greater than' is not well defined, even though numbers might be considered. The algebraic closure of the Reals, the Complex numbers, have no ordering. In fact there is only one complete ordered field, the Reals. 'Greater than', along with 'equals' and 'less than' are all examples of relations. Not equivalence relations (though equals is), relations. Such constructs do not require an ordering and can apply to more general or abstract concepts. Asking if two numbers relate to one another is different from saying if one is bigger than the other, it is more general. A more general class of constructs which have relations partially defined on them are Posets, or Partial Ordered Sets. Another concept which doesn't require the notion of zero. Some constructs don't even involve relations.
hmmm....
you still miss the fundamental logic, for even logic to be true and valid, absolute zero is the universal reference.
eg. "for if something is illogical it makes NO [zero] sense"
Of course if one wishes to launch a contraversial subject that implicates such a massive field of intellectual endeavour one must allow for a long "teething" period.
As far as your contras please provide an example of any set, group , or category usage that doesnot require zero implied or other wise to determine it's validity, partial validity or falacy and I will donate the 200 USD to a worthwhile charity. In fact I will extend the offer by adding if you prove me right I will donate $300 USD to a worthy charity...
Try this: Any value regardless of usage requires zero for that value even in abstract, to be able to be qualified or quantified or even dequalified or dequantified.