A Noncontinuous Limit of a Sequence of Continuous Functions
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Consider a sequence of continuous real-valued functions of a real variable. The sequence
converges pointwise on a set
to a function
if for each
in
,
as
. The limit
is not guaranteed to be continuous; in this Demonstration the limit has a removable discontinuity. (To construct a limit that is discontinuous everywhere in
, construct
with spikes at all numbers that can be written in the form
, where
and
are positive integers and
.)
Contributed by: George Beck (March 2011)
Open content licensed under CC BY-NC-SA
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