, the infamous 'dx
'. In Differential calculus
, one finds differential amounts in the numerator
of the limit definition of differentiation. In Integral calculus
, each addend
in the infinite Riemann sum
definition is a differential amount.
Mathematicians rarely like to talk about differential amounts because they have no particular value - they are just REALLY SMALL, a limiting element for situations where the limit is outside the set*. Yet, if you add an infinite number of them together (integration), or divide one by another (differentiation), you can get a normal number back.
When mathematicians do talk about differential amounts, it is the calculus of differential forms.
*What is the smallest number higher than zero? If you take the limit of these, you get zero... but zero isn't higher than zero, and so doesn't qualify! So dx can't be described by a limit, even though its primary uses are described by limits. Very aggravating for the mathematicians.