# One sided limit of an increasing function defined on an open interval

Let $f:(a,b)\to \mathbb{R}$ be a purely raising function. Does the restriction $\lim_{x\to a^+}f(x)$ always exist and also is an actual number or $-\infty$? If so, is it real that $\ell=\lim_{x\to a}f(x)\le f(x) \ \ \forall x\in (a,b)$? Please give evidence.

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2022-07-25 20:43:22
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