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This is effectively how dual numbers work! https://en.wikipedia.org/wiki/Dual_number https://en.wikipedia.org/wiki/Dual_number
by archermarks 2mo ago
This is effectively how dual numbers work! https://en.wikipedia.org/wiki/Dual_number https://en.wikipedia.org/wiki/Dual_number
- ogogmad 2mo agoDual numbers are basically big/little O notation. They combine beautifully with Robinson's NSA to give the most 18th century-like approach to deriving integral/derivative formulas that I know. And it's fully rigorous!
- srean 2mo agoTrue. Knuth had a paper where he suggests using (a slightly modified) O notation for teaching calculus. https://www-cs-faculty.stanford.edu/~knuth/calc https://www-cs-faculty.stanford.edu/~knuth/calc From the Arxiv paper: > Students have to memorize a diversity of processes for essentially performing the same task. Is that true for differentiation ? I don't recall having to memorize many things, just how differentiation composes over +,-,×,÷, function composition and the differential of a few standard forms. Symbolic integration, on the other hand, is a whole can of worms.