Let and let .

How do you prove the last two statements of the criteria are equivalent?

2 - There exists such that for every , there exists so that and

3 - There exists and there exist sequences in A such that as , yet

Printable View

- Mar 14th 2010, 08:04 AMCrazyCat87Proof of Non-Uniform Continuity Criteria
Let and let .

How do you prove the last two statements of the criteria are equivalent?

2 - There exists such that for every , there exists so that and

3 - There exists and there exist sequences in A such that as , yet - Mar 14th 2010, 08:49 AMPlato
Assume #2. Then to prove #3 let for each .

Assume #3. Then for each some term of must have absolute value less than .

.