Proving calculus concepts with set theory/sequences

[Cinitiator]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

Googling, without much success.

 

[Undoubtedly0]

Generally I believe this field is known as mathematical analysis, or simply analysis (see http://en.wikipedia.org/wiki/Mathematical_analysis).