函數的極限

(ε, δ)-Definition of limit 

Let f be a function. To say that

means that f(x) can be made as close as desired to L by making the independent variable x close enough, but not equal, to the value c.

The (ε, δ)-definition of the limit of a function is as follows:

         Let f be a function defined on an open interval containing c (except possibly at c) and let L be a real number.
Then the statement

means

for all real ε > 0 there exists a real δ > 0 such that for all x with 0 < |x − c | < δ, we have
|f(x) − L| < ε,

or, symbolically,

註：極限的基本運算性質