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Nilpotent infinitesimals allow you to define objects like the “double point”, elocon bangkok, Find elocon on internet, which is the solution set of x2 = 0 on the line. Intuitively, order elocon in us, Purchase elocon without prescription, the double point is the point x = 0, plus another point infinitesimally close to it, cheap elocon tablets. Order elocon without prescription, We can mimic this in nonstandard analysis by considering the solution set to x(x-h) = 0, where h is an infinitesimal, buy elocon in canada. Cheapest generic elocon, This has the property that if you evaluate any differentiable f at h, you get
f(h) = f(0) + f'(h) + o(h), elocon without rx, Buy elocon overnight delivery,
which also holds for nilpotent infinitesimals if you drop the o(h) term. (Here, a nonstandard number k is o(h) if k/h is infinitesimal.)
We can follow the same route to define the intersection of two double lines in the plane as the solution set to x(x-h) = 0 and y(y-k) = 0 where h and k are infinitesimals, buy elocon without prescription. In this case, elocon order, Elocon for order, we get a subtle difference from the nilpotent infinitesimal definition as the solution set for x2 = 0 and y2 = 0. In nonstandard analysis, cheap elocon without prescription, Elocon canada, xy is necessarily o(h) and o(k). If we neglect lower-order terms, generic elocon, Find elocon no prescription required, we get the additional equation xy = 0 which is not satisfied by the intersection of two double lines defined using nilpotent infinitesimals. So seemingly we can't simulate the intersection of two double lines using nonstandard analysis, generic elocon cheap. Buy elocon without prescription, (Reasonably, you might think that maybe the nilpotent infinitesimal definition is just wrong, and that the intersection of two double lines really does morally satisfy the equation xy = 0. Find cheap elocon online, Just counting points, the intersection of two double lines should be some sort of quadruple point, elocon online stores. Order cheap elocon, For an ordinary set of n points, the ring of all differentiable functions from a set of four points to the real line is a vector space of dimension n. Nilpotent infinitesimals preserve this property: the ring of differentiable functions on the intersection of two double lines is a vector space of dimension 4, spanned by 1, x, y, xy. The nonstandard simulation by neglecting lower-order terms gives you a vector space of only dimension 3, spanned by 1, x, y.)
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