I honestly don't know why infitesimals aren't widespread. It can basically have the same basis/justification can't it? But with the bonus of being more intuitive.
You don't even need to use "infinity", it starts out as just a variable representing some unknown quantity, then you "round to zero" on output.
I actually collected a bunch of old Infinitesimal calculus math books.
I honestly don't know why infitesimals aren't widespread. It can basically have the same basis/justification can't it? But with the bonus of being more intuitive.
Indeed they are more intuitive, people like Newton and Leibniz invented/discovered calculus by thinking in terms of infinitesimals, but it took time to be made rigorous, in the XX century. By then network effects got we stuck with epsilons and deltas, given that was the approach made rigorous earlier, and broadly adopted, despite being more cumbersome.
They are in the attic at the moment, but they are all fairly old books (and terse, dry, basic formatting/illustration), seemingly from a period in time when infitesimals were apparently more popular.
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I honestly don't know why infitesimals aren't widespread. It can basically have the same basis/justification can't it? But with the bonus of being more intuitive.
You don't even need to use "infinity", it starts out as just a variable representing some unknown quantity, then you "round to zero" on output.
I actually collected a bunch of old Infinitesimal calculus math books.
Indeed they are more intuitive, people like Newton and Leibniz invented/discovered calculus by thinking in terms of infinitesimals, but it took time to be made rigorous, in the XX century. By then network effects got we stuck with epsilons and deltas, given that was the approach made rigorous earlier, and broadly adopted, despite being more cumbersome.
Would you mind giving us the titles of those books?
They are in the attic at the moment, but they are all fairly old books (and terse, dry, basic formatting/illustration), seemingly from a period in time when infitesimals were apparently more popular.
There are a few similar ones on IA, e.g.
https://archive.org/details/in.ernet.dli.2015.148501/page/n8...
On that page the 'h' term is the infitesimal, as in
Though I prefer something like 'Δx' to make the link to x more explicit. Would love to see a more modern book on the topic.