` ::: Like I said above, mathematicians often describe why one tool will not work, particularly if they are introducing another.  If I read an article that introduces a new notion of infinitesimal, then I would expect some discussion about what is different from the other common notions, and a justification of why there needs to be another.  I don't think it makes sense to have an article about ``inadequacy``, I just don't think these comments deserve inclusion in this article.  ::: Let's talk about the mathematics.   ::: I still would like to know why the insistence on pointing out that the Dixmier trace involves an ultrafilter (and hence the axiom of choice).  The implication of the comments above would be that if this were true then Connes made an error.  What error does it imply?   `