MathematicalPhysicist
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how does weierstrass' approach to analysis differ from the classical approach, i.e leibnizs' and newton's calculus?
I said that Weierstrass SYSTEMATIZED the use of this technique; I didn't say he was the the first to have these ideas.quasar987 said:And how does Cauchy fit in that picture? I thought he was the one who invented the epsilon-delta formulation
from what i read his approach had left behind the infinitisemals for the the epsilon-delta formulation, but i also read that abraham robinson had resurrected the infinitisimal formulation on a better rigorous formulation, in what now is called Non-Standard Analysis (NSA), how do these approaches differ from eachother, and what makes NSA non-standard?arildno said:Since Weierstrass was the one systematizing the "epsilon/delta"-approach to calculus, you might say that Weierstrass was the first to provide a truly mature and rigorous approach to calculus.
I hope math-wizzes like Hurkyl, M.G, or mathwonk can give you a bit of solid info on robinson's approach, but here's a few schematic details on the history of analysis that I don't think is too misleading:loop quantum gravity said:from what i read his approach had left behind the infinitisemals for the the epsilon-delta formulation, but i also read that abraham robinson had resurrected the infinitisimal formulation on a better rigorous formulation, in what now is called Non-Standard Analysis (NSA), how do these approaches differ from eachother, and what makes NSA non-standard?
Real numbers can be constructed from natural numbers. Hyperreal numbers, extensions of the real numbers on which non-standard analysis is based, are constructed from non-standard models of the natural numbers.loop quantum gravity said:from what i read his approach had left behind the infinitisemals for the the epsilon-delta formulation, but i also read that abraham robinson had resurrected the infinitisimal formulation on a better rigorous formulation, in what now is called Non-Standard Analysis (NSA), how do these approaches differ from eachother, and what makes NSA non-standard?