"

 The very concept of ""discrete mathematics"" itself is a vague illusion  

The thing is, analysis is like anything else in mathematics. It can be built up from the basic principles of counting. That is, the simplest principles that build the addition function, which we think of as the number of elements in a union of finite disjoint sets of given sizes, and the multiplication function, the exponentiation function, etc, and anything required for general talk of ""the"" number of objects corresponding to some act of counting, that is, to prove that it is well defined. These basic counting principles are responsible for all of mathematics, including analysis. There is only one mathematics. There is no distinction between discrete and continuous mathematics that is not exposed as an illusion if you look hard enough. There are no walls. 

It's fine to think about discrete mathematics in the same sort of loose way that people think about the distinction between number theory and combinatorics. For example, the Goldbach conjecture is easily stated combinatorially, and that's fine as long as you recognise the inherent looseness in what these two areas of mathematics represent. An article about ""discrete mathematics"" can never be very good. All it can say, is that discrete mathematics is a hodgepodge of areas of mathematics which do not implictly involve the areas of real or complex analysis, or topology, for their study. Anything else would be far from the truth. I say ""implicitly"", because real and complex analysis, and topology to some extent, can be very useful in these areas."