I read with interest your article. Here are few points worth to mention:

1. IDF is defined as log(D/d) where D is number of documents in a collection and d is the number of documents mentioning a given term, regardless if the documents are relevant to said term. The base of the log does not matter (it can be base 10, 2, etc). The reason for taking logs is because most scoring functions in IR are assumed to be additive and because terms are assumed independent form one another (even when often this is not exactly the case).

2. IDF is a measure of the discriminatory power of a term (term specificity), but it does not relevancy. Indeed, IDF is a term weight score in the absence of relevance information.

3. IDF is a small pixel in the bigger picture of Robertson-Sparck Jones Probabilistic Model (RSJ-PM). A tutorial on the RSJ-PM Model explaining this model is available at http://www.miislita.com/.

4. With unstructured, unfocused, and generic collections at the scale of the Web (e.g. commercial search engines like Google), the stability of IDF and this as a reliable scoring function has been put into question by several authors.

Regards

Dr. Edel Garcia
http://www.miislita.com/