Take the 2-minute tour ×  Declaring that a set has 10 elements
requires two things:    • find some elements   • show they are
all distinct   • showing you have all of them  Sometimes these
are easier said than done.  E.g. count all the triangles  E.g.
count all the Republicans in Nebraska  E.g. count all the files
in this database  Is there a theory of enumeration for when you
are too lazy (or lack the resources) to check your list of
elements is distinct an exhaustive?  EDIT I'm not even 100% sure
what I am looking for here.  I know that in current technology
trends, the idea of "cardinality" is being somewhat challenged.
If one could go through all your bins and index all the pieces
of information being stored, it would be possible to give an
order of magnitude estimate. There are situation where the
amount of information being stored is so large and unpredictible
that it's not even possible to do that. Enter probabilistic
counting.  The task is to count all the elements in your
database that satisfy proper