Negating "For All" Statement: Proving False

[keemosabi]

Homework Statement

Negate the following statement and thereby prove that it is false.
[PLAIN]http://img834.imageshack.us/img834/5020/74520479.png

Homework Equations

The Attempt at a Solution

I know the general rules but there are so many conditions in this statement that I don't know how to apply them.

My guess right now would be to change all the "for all" statements to "there existst" and to reverse the direction of the last inequality.

 

[HallsofIvy]

Homework Statement

Negate the following statement and thereby prove that it is false.
[PLAIN]http://img834.imageshack.us/img834/5020/74520479.png

Homework Equations

The Attempt at a Solution

I know the general rules but there are so many conditions in this statement that I don't know how to apply them.

My guess right now would be to change all the "for all" statements to "there existst" and to reverse the direction of the last inequality.

Not exactly "reverse it". "<" should become "$\le$". Also that "there exist $\delta> 0$" should become "for all $\delta> 0$".

 

[keemosabi]

Not exactly "reverse it". "<" should become "$\le$". Also that "there exist $\delta> 0$" should become "for all $\delta> 0$".

Thank you for the reply. I'm just wondering how you came up with that. Could you elaborate a little please?