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Derivative at a Discontinuity
Alok Singh's Blog
We’ll use the hyperreal numbers from the unsexily named field of nonstandard analysis to offer a radically elementary way of thinking about the problem. If you did this with the usual definition of generalized functions, you wouldn’t figure out how to compute anything with them until about halfway through math grad school. In the realm of nonstandard analysis, infinite numbers aren’t obstacles but stepping stones—bridges that connect the discontinuities of mathematics with the continuity of intuition.
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