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"An equation such as ∫ 3x^2 dx = x^3+C says that we add together uncountably many infinitesimals, and we get a medium-sized number." Yelp! My buddies Riemann &
by enthdegree 12y ago
"An equation such as ∫ 3x^2 dx = x^3+C says that we add together uncountably many infinitesimals, and we get a medium-sized number."
Yelp! My buddies Riemann & Lebesgue had quite a different story on the matter...
- noelwelsh 12y agoNon-standard analysis (e.g. http://www.sjsu.edu/faculty/watkins/infincalc.htm http://www.sjsu.edu/faculty/watkins/infincalc.htm -- another example of awesome web page design) does formalise the concepts of infinitesimals. It's quite neat to have a complete alternate formalism for calculus.
- enthdegree 12y agoThat's really cool. However it's important to note that it nonstandard analysis does not 'live' in the real numbers. It turns out the hyperreals aren't even a metric space! I'm not intimately familiar with them though, and have heard that they are a lot more lucid abstraction for some things when compared to calculus on the reals.
- deleted 12y ago[deleted]