Prove that the reversed quantifiers don't define a limit

[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?

 

[matt grime]

Why not let e be 2?

 

[flying2000]

I don't understand..

Why not let e be 2?

I think it's "there exists e"

 

[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...

 

[Hurkyl]

"there exists e"

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

 

[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.