My question is related to what is the physical content of infinitesimals. In mathematics the infinitesimals as hyperreals (Robinson 1960) are introduced as numbers greater than 0 but smaller than any real number. Can a physical quantity in real nature increase with a such infinitesimal number?
This must be outside physics because it is impossible to measure (each measurement gives a real number - even a rational decimal number). In the end infinitesimal increase can not be proven.