## negation of this statement

I am stuck in trying to take the negation of this statement:

$$(\forall \varepsilon>0)(\exists N \in N)(\forall n,m\geq N)(\forall x \in R [|f_n(x)-f_m(x)|< \varepsilon]$$

One of my thoughts was that in order to move the negation inside the brackets, all I need to do is say $$(\exists \varepsilon \leq 0)$$...and everything else remains unchanged.

However, my other thought was to somehow move the statement $$\varepsilon > 0$$ to the end of the original statement and make it: $$(\varepsilon > 0 \Rightarrow |f_n(x)-f_m(x)|< \varepsilon)$$

If you can help me in anyway, it would be greatly appreciated.

Thanks!
 PhysOrg.com science news on PhysOrg.com >> Galaxies fed by funnels of fuel>> The better to see you with: Scientists build record-setting metamaterial flat lens>> Google eyes emerging markets networks
 Recognitions: Science Advisor It seems like you need something like there exists an eps >0 for which there is no N for the property (a Cauchy sequence in the sup norm topology).
 I figured it out...here is the solution for anyone who is curious. $$(\exists \varepsilon>0)(\forall N \in N)(\exists n,m\geq N)(\exists x \in R [|f_n(x)-f_m(x)| \geq \varepsilon]$$ Thanks for the help!