A World Without Zero

The curious thing about zero in mathematics is that it took so long to develop, mainly because mathematics used to be about counting real world objects rather than abstract problems. The irony is that today, the most accurate measurements and predictions of the real world and how it works now relies on this form of abstracted maths.

Yet, I believe that there is a fundamental flaw at the heart of this system, that zero (or its cousin infinity) does not exist in the real world. If so, is it reasonable to say that any mathematical system that uses those concepts can be accurately applied to the real world?

It appears that the conclusion is that mathematical laws are not supposed to actually define the real world, but something beyond it, something better. This is obvious if considered in detail. Every calculation is an ideal, not completely gritty and realistic. Even simple calculations like the speed of a car, these are idealised. The actual motion might chug one way or the other, affected by this micro pulse of air, this beetle or speck of gravel. Mathematical preditions were always beyond reality.

If that is so, is it fair to assume that such laws can be applied to real and fundamental understanding of the actual universe?

Perhaps a new form of maths without zero needs to be developed, but on what principle?

Perhaps multiplication and division can replace all addition and subtraction. 2-1 is the same as 2/2. 3-2 is the same as 3*0.666 - yet 0.666... to infinity, which is forbidden. Can a mathematical system with no zero or infinity exist? All whole numbers end in an infinite number of zeros. There are 12.0 eggs in a dozen (12.000000000000 to infinity). The fact that these are zero might cancel out the fact that there are an infinite number of them. Similarly with 12.500000000 etc.

Fundamentally, in maths 1-1=0. If in the real universe this is not true, that 1-1>0. How can this be tested?

At some point, extremely small and extremely large scales (1/extremelysmall perhaps!) this effect should be evident, and testable.