Yes, we should have analysis
I may have tipped my hand in asking this question, but I think it would be a good idea. These questions might not be the easiest tag for programming challenges because they often deal with the infinite, but there are still plenty of interesting and unique challenges that could be asked.
Here is a mock up of what the tag description/wiki might look like:
Analysis is the study of limits, convergence, and related concepts such as differentiation and continuity.
This tag is for questions that explore the topics of Mathematical analysis. Analysis has a number of subfields pertaining to more specific topics.
Real analysis is the branch of analysis that is concerned with functions on the Real numbers. It includes topics such as convergence, continuity, metric spaces and smoothness
Complex analysis is concerned with functions of complex variables. Complex analysis is concerned with the extension of the ideas of real analysis into the complex plane. Important topics in Complex analysis include analyticity, branch cuts and residues. Questions about complex numbers but not specifically about analysis should be tagged with complex-numbers.
analysis should be used for topics in these areas as well
I have made this community wiki so anyone may help me complete it as they see fit. I am not very familiar with functional analysis so if someone would like to add a bit about that I would be pleased.