Everywhere Locally UNBOUNDED Function | COUNTEREXAMPLES in Analysis | E5

Is it possible for a function to be unbounded in some neighborhood of every point of its domain? We construct a function that is everywhere locally unbounded. The proof is based on the facts that every rational number can be uniquely represented as a fraction of two integers in lowest terms and that rational numbers are dense in the set of real numbers.

The animations for this video are made in Manim Community Edition, which is a fork of the original Manim package that Grant Sanderson uses to make his videos for the 3blue1brown YouTube channel.

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[MathVisualProofs]

That’s a super cool graph to look at. Nice work here.