Proving calculus concepts with set theory/sequences

1. Jul 1, 2012

Cinitiator

1. The problem statement, all variables and given/known data
How is the field of mathematics which focuses on defining the calculus concepts (such as limits) using the set theory and/or sequences called? Where numbers are seen as discrete, and concepts like limits are defined in these terms.

2. Relevant equations

3. The attempt at a solution
Googling, without much success.

2. Jul 1, 2012