Does the convergence of function for rational and irrational sequences imply its convergence for any real sequence. – math.stackexchange.com

Does the convergence of function for rational and irrational sequences imply its convergence for any real sequence. – math.stackexchange.com

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Given are the following two statements ($x_r$ denotes a sequence of rational numbers, and $x_i$ denotes a sequence of irrational numbers): $$1. \forall x_r \to 1 \implies f(x_r) \to f(1)$$ $$2. \...

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