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Graduate Negating a Universal Statement in Real Analysis
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!- bguidinger
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- Forum: Set Theory, Logic, Probability, Statistics
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Graduate Negating a Universal Statement in Real Analysis
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...- bguidinger
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- Forum: Set Theory, Logic, Probability, Statistics