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ε, the base of the dual numbers.
It’s a nonzero hypercomplex number that squares to zero, enabling automatic differentiation.
Came here to say this, but since it's already here, I'll throw in a bonus mind-melting fact: ε itself has no square root in the dual numbers.
As a not good at math person, advanced math sounds hella fake sometimes. Like almost a parody of math. I accept that it's real but part of me will always think it's some inside joke or a secret society cult for the lamest god.
A lot of "advanced" maths comes from asking "What if this was a thing, how would that work? Would it even work?", so you could say there's a deliberate sense of "fake" about it.
Dual numbers come from "What if there was another number that isn't 0 which when multiplied by itself you get 0?"
Basic dual numbers (and complex numbers) are no harder than basic algebra, shallow end of the pool kind of stuff, but then not everyone is comfortable getting in the water in the first place, and that's OK too.
Thank you for the info!
Puts on floaties and a brave face, then advances to the shallow end
What is the value in learning about "What if there was another number that isn't 0 which when multiplied by itself you get 0?"
Are there any practical applications IRL for dual numbers?
Edit: Screw Screw theory. Wikipedia says dual numbers have applications in mechanics and to see Screw Theory. I tried reading about it and my eyes glazed over so quickly. Math so isn't for me lol.
Since there's a reasonably strong link to calculus, and mechanics as you've already found, it could theoretically help in physics simulations either in a computer or on paper.
As for practical application, well, emulating physics is pretty important in a lot of computer games, or getting robots (assembly line arms, androids, automated vacuum cleaners) around the place and to do what they need without accidentally catapulting themselves into next Tuesday.
How that's actually programmed might not involve dual numbers at all, but they're one way of looking at how those calculations might be done.
Complex numbers 🤝 Split-complex numbers 🤝 Dual numbers
All super rad.