mathematics, a limiting case of a
mathematical object is a
special case that arises when one or more components of the object take on their most extreme possible values.
statistics, the limiting case of the
binomial distribution is the
Poisson distribution. As the number of events tends to infinity in the binomial distribution, the random variable changes from the binomial to the Poisson distribution. A
circle is a limiting case of various other figures, including the
Cartesian oval, the
superellipse, and the
Cassini oval. Each type of figure is a circle for certain values of the defining parameters, and the generic figure appears more like a circle as the limiting values are approached.
Archimedes calculated an approximate value of
π by treating the circle as the limiting case of a
regular polygon with 3 × 2 sides, as n n gets large. In
electricity and magnetism, the
long wavelength limit is the limiting case when the
wavelength is much larger than the system size. In
economics, two limiting cases of a
demand curve or
supply curve are those in which the
elasticity is zero (the totally inelastic case) or infinity (the infinitely elastic case). In
continuous compounding is the limiting case of compound interest in which the compounding period becomes infinitesimally small, achieved by taking the limit as the number of compounding periods per year goes to infinity.
A limiting case is sometimes a
degenerate case in which some qualitative properties differ from the corresponding
properties of the generic case. For example: