I found some remarkable property of the Vandermonde determinant. Based on this property we are able to introduce a notion "difference between n>2 quantities". Below I give the abstract of this result.
The notion of difference between two quantities plays a basic role in mathematics, consequently in all branches of human activity where the mathematics is applied. However the long stand question is: what is {\it the difference between three (or more) quantities}? The binary operation $[a,b]=(a-b)$ possesses the following principal feature: with respect to the third quantity $c$ this operation is decomposed into a sum of the same operations between $a$ and $c$, and $c$ and $b$, i.e., $$ [a,b]=[a,c]+[c,b]. $$ Denote by $[a,b,c]$ difference between three quantities $a,b,c$. With respect to additional quantity $d$ this definition of the difference has to possess with the following property $$ [a,b,c]=[d,b,c]+[a,d,c]+[a,b,d]. $$ We prove that this property of difference between three (or $n\geq 2$) quantities is satisfied by one of the features of Vandermonde determinant.
