points of discontinuity for the function f(x) = x + [x] (bracket function)
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Analyze the cases $\displaystyle a\in \mathbb{Z}$ and $\displaystyle a\not\in \mathbb{Z}$ .
As per your guidance f(x) is discont as x belongs to Z but how we analyze for x doesnot belong to Z
Suppose $\displaystyle a\in(n,n+1)$ with $\displaystyle n\in\mathbb{Z}$ then, in a neighborhood $\displaystyle V(a)$ of $\displaystyle a$ we have $\displaystyle f(x)=x+\lfloor x \rfloor=x+n$ .
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