- #1
ait.abd
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Homework Statement
Find a sequence of continuous functions [tex]f_n: R \rightarrow R[/tex] such that [tex]lim_{x \rightarrow 0}lim_{n \rightarrow \infty}f_n(x) [/tex] and [tex]lim_{n \rightarrow \infty}lim_{x \rightarrow 0}f_n(x) [/tex] exist and are unequal.
Homework Equations
N/A
The Attempt at a Solution
I think I need a sequence of continuous functions that has a limit function which is continuous at zero but discontinuous at some other point. In that case, the sequence of functions will not be uniformly convergent and we will not have these limits equal. But I don't know what function can fulfill this criteria.