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Let $f:\mathbb R\to\mathbb R$, $$f(x)=\begin{cases}0,&x=0\\1,&\text{otherwise}\end{cases}$$ Show that $f$ is discontinuous for all $x\neq 0$. Wts: $\forall\epsilon>0,\exists\delta>0,\forall x\in\mathbb R$, $|x-a|<\delta\implies |f(x)-1|<\epsilon$
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Sat, 04 Jan 2020 05:12 GMT