If I want to write the negation of $\lim_{x\to c}f(x)=L$, is it considered incorrect to write $\lim_{x\to c}f(x) \ne L$ (because this indicates that the limit exists)?
meaning of $\lim_{x\to c}f(x)\ne L$
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$\begingroup$
limits
notation
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0I would say that it is indeed incorrect. – 2017-01-16
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0@Omnomnomnom Thanks for your feedback. – 2017-01-16
1 Answers
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The negation would be that for any sequence $\{x_n\}$ converging to $c$, we have that the sequence $\{f(x_n)\}$ does not converge to $L$.
If $\lim_{x \to c} f(x)$ does not exist, then the statement \begin{align*} \lim_{x \to c} f(x) \neq L \end{align*} has no meaning.