Interesting conversation. Calculus uses the concept of infinitesimals (quantities smaller than any real number but not zero) and limits to get around the problem of discrete steps and continuous change and to model smooth, continuous reality using mathematical approximations. However, I believe discrete mathematics has more practical applications in the real world.
This has been the topic of a lot of conversation in the Mathematical foundations community, including things like constructivist mathematics https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics).
One of the most interesting researchers along these line is Norman Wildberger. He has a very extensive collection of YouTube videos addressing the proper foundations of a wide range of mathematical fields. Perhaps a good starting point is https://www.youtube.com/watch?v=91c5Ti6Ddio&list=PLIljB45xT85DGxj1x_dyaSggbauAgrB6R.
Interesting conversation. Calculus uses the concept of infinitesimals (quantities smaller than any real number but not zero) and limits to get around the problem of discrete steps and continuous change and to model smooth, continuous reality using mathematical approximations. However, I believe discrete mathematics has more practical applications in the real world.