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 January 9th, 2014, 09:58 AM #1 Member   Joined: Jan 2013 Posts: 96 Thanks: 0 Function Is there any function $f: \mathbb{R} \to \mathbb{R}$ with the property that $\forall x \in \mathbb{R}, \exist (x_n)_n$ with $\lim_{n \to \infty}x_n=x$ such that $\lim_{n \to \infty} f(x_n)= \infty$?
 January 11th, 2014, 08:13 AM #2 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: Function Perhaps $f(x)= \frac{1}{x}$ with the sequence attached being $\lim_{n \to \infty} x_n= 0$?
 January 11th, 2014, 10:26 AM #3 Member   Joined: Jan 2013 Posts: 96 Thanks: 0 Re: Function Well, in your example there is a sequence (x_n) with $x_n \to x$ such that $f(x_n) \to \infty$ just for x=0 (not for all $x \in \mathbb{R}$)!
 January 11th, 2014, 11:03 AM #4 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: Function I see, I may have overlooked that condition. Nice question, by the way.
 January 17th, 2015, 12:24 AM #5 Newbie   Joined: Jan 2015 From: fsd Posts: 1 Thanks: 0 I solved it! I forgot about .

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