- #1

- 13

- 0

Given ε > 0 there exists a [itex]\delta[/itex] > 0 such that |x – a| < [itex]\epsilon[/itex] [itex]\Rightarrow[/itex] |f(x) – f(a)| < [itex]\delta[/itex]

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter gregy6196
- Start date

- #1

- 13

- 0

Given ε > 0 there exists a [itex]\delta[/itex] > 0 such that |x – a| < [itex]\epsilon[/itex] [itex]\Rightarrow[/itex] |f(x) – f(a)| < [itex]\delta[/itex]

- #2

mathman

Science Advisor

- 7,942

- 496

There will always exist δ. For example f(x)=0 for x< 0 and f(x) = 1 otherwise. Then your definition will have continuity at 0 using δ > 1.

Share: