123 與 XYZ 的相遇

關於極限的四則運算 內文

 

註：【 Precise statement of limit of a function 】

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,

The real inequalities exploited in the above definition were pioneered by Bolzano and Cauchy and formalized by Weierstrass.