Electrical resistivity and conductivity results in the important concept of "quasineutrality", which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma ("n" = <Z>"n"), but on the scale of the Debye length there can be charge imbalance. In the special case that "double layers" are formed, the charge separation can extend some tens of Debye lengths. The magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density. A common example is to assume that the electrons satisfy the Boltzmann relation: Differentiating this
Positive real numbers excess has been reciprocated. For formula_15 the sequence terminates with an exact fractional expression of formula_16, and for quadratic irrational formula_16 the sequence becomes a periodic continued fraction. In the study of classical groups, for every formula_18, the determinant gives a map from matrices over the reals to the real numbers formula_19 Restricting to invertible matrices gives a map from the general linear group to non-zero real numbers: formula_20. Restricting to matrices with a positive determinant gives the map formula_21; interpreting the image as a quotient group by the normal subgroup relation expresses the positive reals as a Lie group.