Una tentazione affascinante
We discuss several aspects of infinity in the history of mathematics.
math.HO↗
arXiv subjects
Claudio Bernardi
Publications and source records attributed to Claudio Bernardi.
Graphs of real functions with pathological behaviors
This paper deals with constructions and properties of unusual function from R to R, as discontinuous additive functions and everywhere surjections.
math.HO↗
What Mathematical Logic Says about the Foundations of Mathematics
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us to explain mathematical activity; the point is to discuss what and in which sense logic can "explain". For example, let's consider the basic concept of an axiomatic system: an axiomatic system can be very useful to organize, to present, and to clarify mathematical knowledge. And, more importantly, logic is a science with its own results: so, axiomatic systems are interesting also because we know several revealing theorems about them. Similarly, I will discuss other topics such as mathematical definitions, and some relationships between mathematical logic and computer science. I will also consider these subjects from an educational point of view: can logical concepts be useful in teaching and learning elementary mathematics?
math.HO↗
Un problema da discutere: un inganno con le percentuali
We discuss a non-intuitive situation concerning percentages.
math.HO↗
Un problema da discutere: una rappresentazione geometrica del teorema del coseno
We present, discuss and generalize an elegant geometrical proof of the law of cosines, due to Al Cuoco.
math.HO↗
Gli angoli alla base di un triangolo isoscele
This paper deals with the celebrated Euclidean theorem about isosceles triangles, comparing different proofs.
math.HO↗