What ' s it called when a tax is levied on certain goods and commodities produced or sold within a country and on licences granted for certain activities ? Excise Gary <| sep |> It is not yet proved that pie is irrational , and more generally it remains unproved that pi and e are linearly independent over Q . While it is unrealistic to imagine that these two numbers would match up at some point , that has not been rigorously refuted yet . You say algebraic independence means no polynomial px with rational coefficients has pe pi , but that ' s not really enough . There ' s also no such px making psqrt 2 sqrt 3 but we do consider sqrt 2 and sqrt 3 to be algebraically dependent . Algebraic independence means there ' s no nonzero polynomial in two variables px , y with rational coefficients such that pe , pi 0 . Thus sqrt 2 and sqrt 3 are algebraically dependent , using px , y 3 x 2 2 y 2 .