Draft:Antonio De Zolt

Antonio De Zolt (Conegliano, 8 August 1847 – Milan, 5 February 1926) was an Italian mathematician, famous for his eponymous postulate.

Biography
Graduated from the University of Turin in 1872, he became a professor at the Regio Liceo Ginnasio Giuseppe Parini in Milan. He dedicated himself to the study of Geometry. He is buried in a niche at the Monumental Cemetery in Milan. In 1895, he was one of the founders (with Aurelio Lugli and Rodolfo Bettazzi) of Mathesis, an Italian society dedicated to the teaching of Mathematics.

De Zolt's Postulate
Euclid's axioms include the following:

"The whole is not equivalent to a part of it."

This axiom is intuitively valid for finite objects, but if we compare infinite ones it is no longer true. Although Euclid was talking about geometry, it is easier to intuitively see why this is so if we consider the example of the infinite natural numbers. For each natural number, we can pair it with its double, so that each natural number corresponds to an even number. Therefore, we can deduce that there are as many even numbers as there are natural numbers. But the even numbers are a part of the natural numbers, so they should not be equivalent; this result is thus contrary to the axiom stated by Euclid. Even in the geometrical case this axiom can fail: see the Banach–Tarski paradox in three-dimensional space.

In 1881, De Zolt enunciated a special case of this axiom from Euclid concerning the equivalence of polygons:

If a polygon is divided into parts in a given way, it is not possible, when one of these parts is omitted to recompose the remaining parts in such a way that they cover entirely the polygon.