  The goal of this work is to introduce and study fuzzy limits of functions.
Two approaches to fuzzy limits of a function are considered. One is based on
the concept of a fuzzy limit of a sequence, while another generalizes the
conventional epsilon-delta definition. It is demonstrated that these
constructions are equivalent. Different properties of fuzzy limits of functions
are found. Properties of conventional limits are easily deduced from properties
of fuzzy limits. In the second part of this work, the concept of fuzzy limits
of a function is extended to provide means to define nontrivial continuity of
functions on discrete sets. In addition, fuzzy limits of functions are
introduced and studied.
