# A limit definition problem.

1. Sep 29, 2004

### flying2000

show by example that the stament
for all d>0 there exists e>0 such that o<|x-a|<d ->
|f(x）-L|<e is Not the definition of limit.

would somebody give me a hint?

2. Sep 30, 2004

### matt grime

Why not let e be 2?

3. Sep 30, 2004

### flying2000

I don't understand..

I think it's "there exists e"

4. Sep 30, 2004

### matt grime

I take it that means you didn't understand the hint?

Ok, the function f(x)=2 for all x in R is obvioulsy continuous. Take your known incorrect definition, take my hint and think....

5. Sep 30, 2004

### Hurkyl

Staff Emeritus
If you can do it by setting e = 2, then this clause is certainly satisfied.

6. Sep 30, 2004

### mathwonk

how can you answer this without a definition of limit? a more meaningful question would be to also give the definition of limit and then ask for a function and number that satisfies one definition and not the other.