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Proposition: Limit of the Identity Function
Let $f:\mathbb R\to\mathbb R,$ $f(x)=x$ be a real identity function. Then for every $a\in\mathbb R,$ $\lim_{x\to a }f(x)=\lim_{x\to a }x=a.$
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References
Bibliography
 Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016