Recent content by MathStudent999

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    Graduate Help with understanding why limit implies uniqueness

    I'm studying ODEs and have understood most of the results of the first chapter of my ODE book, this is still bothers me. Suppose $$\begin{cases} f \in \mathcal{C}(\mathbb{R}) \\ \dot{x} = f(x) \\ x(0) = 0 \\ f(0) = 0 \\ \end{cases}. $$ Then, $$ \lim_{\varepsilon \searrow...