Heine Definition of Continuity
Continuity of Functions A real function f (x) is said to be continuous at
it holds that
In practice, it is convenient to use the following three conditions of continuity of a function f (x) at point x = a: 1. Function f (x) is defined at x = a; 2. Limit 3. It holds that Cauchy Definition of Continuity ( Consider a function f (x) that maps a set
the value of f (x) satisfies:
|
(
is the set of real numbers), if for any sequence 
such that
exists;
.
- Definition)
there exists some number 
such that for all 
with
