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Tool Like Argument Principle For Real-Valued Functions
The Argument Principle gives a way of numerically counting the number of roots-poles ($Z-P$) of a meromorphic function in a contour. I was wondering, can the Argument Principle (or some other tool ...
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Find the closest/next $x\in\mathbb{N}$ that satisfies the equation $Ⲭ_{\mathbb{N}}(f(x)) = 1$.
Find the closest/next $x\in\mathbb{N}$ that satisfies the equation $Ⲭ_ℕ(f(x)) = 1$, where $Ⲭ_\mathbb{N}(x): \mathbb{R} \rightarrow \mathbb{N}$ is defined by
$$
\begin{cases}
1 &\text{if } f(x) \...