Mathematics

Problem

A function

f

R

into itself is continuous at a point

a

R

, iff for each

\epsilon > 0

, there exists,

\delta > 0

such that (a)

|f(x) - f(a)| < \epsilon \Rightarrow |x - a| < \delta

(b)

|f(x) - f(a)| > \epsilon \Rightarrow |x - a| > \delta

(c)

|x - a| > \delta \Rightarrow |f(x) - f(a)| > \epsilon

(d)

|x - a| < \delta \Rightarrow |f(x) - f(a)| < \epsilon