Is there a way to make sense of the following statement: "[itex]f[/itex] is continuous at a point [itex]x_0[/itex] such that [itex]f(x_0) = \infty[/itex]?" The standard definition of continuity seems to break down here: For any [itex]\epsilon > 0[/itex], there is no way to make [itex]|f(x_0) - f(x)| < \epsilon[/itex], since this is equivalent to making [itex]|\infty - f(x)| < \epsilon[/itex], which cannot happen, since [itex]\infty - y = \infty[/itex] for every [itex]y\in \mathbb R[/itex] and [itex]\infty - \infty[/itex] is undefined. So is there any way to make sense of continuity of an extended real-valued function at a point where it's infinite?(adsbygoogle = window.adsbygoogle || []).push({});

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# Making sense of continuity at a point where f(x) = Infinity?

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