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Is the following true?

If $\liminf_{x\to\infty}f(x)>c$, where $c>0$,

then:

given $\epsilon >0$ there exist $x_{\epsilon}>0$ such that $f(x)>c+\epsilon$ , for all $x\geq x_{\epsilon}$.


The thing that I know is that: there exist $x_{o}>0$ such that $f(x)>c$ , for all $x\geq x_{o}$, (so no $\epsilon$ involved!)

2 Answers 2