Differentials in Calculus.

1. Mar 7, 2015

Timothy S

I have recently come across the use of differentials in visualizing and thinking about calculus. In this method, one thinks of dx/dy as an actual fraction of infinity small yet real numbers. How is it possible to apply this to implicit functions?

2. Mar 8, 2015

pwsnafu

Contradiction in terms. Every real number is finite by definition. What you can do is consider non-real numbers that satisfy $0<\epsilon<r$ for every real number r. This is the core of infinitesimals.