Editing Pisot–Vijayaraghavan number (section)

===Elementary properties===
* Every integer greater than 1 is a PV number. Conversely, every [[rational number|rational]] PV number is an integer greater than 1.
* If α is an [[irrational number|irrational]] PV number whose minimal polynomial ends in ''k'' then α is greater than |''k''|.
* If α is a PV number then so are its powers α<sup>''k''</sup>, for all positive integer exponents ''k''.
* Every real [[algebraic number field]] '''K''' of degree ''n'' contains a PV number of degree ''n''. This number is a field generator. The set of all PV numbers of degree ''n'' in '''K''' is closed under multiplication.
* Given an upper bound ''M'' and degree ''n'', there are only [[finite set|finitely many]] of PV numbers of degree ''n'' that are less than ''M''.
* Every PV number is a [[Perron number]] (a real algebraic number greater than one all of whose conjugates have smaller absolute value).