- In mathematics, a
nowhere continuous function, also
called an
everywhere discontinuous function, is a
function that is not
continuous at any
point of...
-
restricting to
sufficiently small changes of its argument. A
discontinuous function is a
function that is not continuous.
Until the 19th century, mathematicians...
-
sequence of
functions meeting the
requirement that
converges to a
discontinuous function. For this,
modify an
example given in
Inner product space#Some examples...
- ( x ) {\displaystyle H(x)} is the
Heaviside step
function. As with most such
discontinuous functions,
there is a
question of the
value at the transition...
-
result is not true however; that is, a
discontinuous function may be
locally bounded. For
example consider the
function f : R → R {\displaystyle f:\mathbb...
- distributions.
Generalized functions are
especially useful for
treating discontinuous functions more like
smooth functions, and
describing discrete physical...
- uniformly. The
pointwise limit of a
sequence of
continuous functions may be a
discontinuous function, but only if the
convergence is not uniform. For example...
-
differentiability of g is due to Paul du Bois-Reymond. The
given functions (f, g) may be
discontinuous,
provided that they are
locally integrable (on the given...
-
derivative would then be
discontinuous on the measure-0 set C
instead of the positive-measure set S, and so the
resulting function would have a
Riemann integrable...
- {\displaystyle x_{0}} at
which f {\displaystyle f} is
discontinuous.
Consider the
piecewise function f ( x ) = { x 2 for x < 1 0 for x = 1 2 − x for ...
