Mathematical Economics

After some brief discussion of the course's scope and aims, as well as of some prerequisite notions, we begun with the definition of a distance function (metric) w.r.t. a non empty set of reference as a real function defined on the product of this set with itself that satisfies positivity, separation, symmetry and triangle inequality. The example of the discrete metric showed that any such set bears at least one such function, and further examples implied that more than one metrics can exist, possibly inside structured families, some of which attribute possibly different properties to the reference (or carrier) set. The structured set comprised of the carrier set with the metric was defined as a metric space.  We have begun the examination of several examples of such spaces. Details can be found at the course's syllabus, notes on the previous here, and a counterexample of a metric here.