Since additive constant terms in objective functions do not affect optimal decisions, the term 1 in the numerator can be, and usually is, omitted ( except when establishing the limiting case of \ ln ( c ) as below ).
32.
This 2007 result by Mikhail Katz, Mary Schaps, and Uzi Vishne improves an inequality due to Peter Sarnak and Peter Buser in the case of arithmetic groups defined over \ mathbb { Q }, from 1994, which contained a nonzero additive constant.
33.
(Of course, the condition that " b " be the negative of the gradient of ? only determines ? up to an additive constant; this constant may be chosen so that exp ( & minus; 2? ( ?) ) is a probability density function with integral 1 .)
34.
The generalization of this equation is Clausius theorem, which suggests the existence of a state function " S " ( i . e ., a function which depends only on the state of the system, not on how it reached that state ) defined ( up to an additive constant ) by
35.
As our electric potential article explains : " The potential energy and hence also the electric potential is only defined up to an additive constant : one must arbitrarily choose a position where the potential energy and the electric potential are zero . " talk ) 19 : 17, 1 September 2010 ( UTC)
36.
Because of the ambiguity of ? up to the addition of any integer multiple of 2?, any continuous choice of ? on U will suffice to define an antiderivative of 1 / z on U . ( It is the fact that ? cannot be defined continuously on a simple closed curve containing the origin in its interior that is the root of why 1 / z has no antiderivative on its entire domain !-{ 0 } . ) And because the derivative of an additive constant is 0, any constant may be added to the antiderivative and it's still an antiderivative of 1 / z.
