These mathematical "abstractions" are not the same as "abstractions" in natural sciences: they are only a succinct notation that provides leverage to perform mo

These mathematical "abstractions" are not the same as "abstractions" in natural sciences: they are only a succinct notation that provides leverage to perform more reasoning with less writing, not a simplified and separate model of a system. For example, positional notation decreases the size of natural number representations exponentially compared to straightforward application of Peano's axioms or the like, but the numbers themselves remain exactly the same.