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Lecture 7

Lecture 7 . Surreal Numbers. The Construction of R from Q . Recall that the set of reals R can be constructed from the set of rationals Q using Cauchy sequences.

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XM=(XL+XR)/2

The mechanics of Newton, Bi-section, and Secant methods. Use 3 its of Newton to fine the root of f(X)=X 2 -3 near X =1. X=Xold +( -F/Fdash). Use 3 its of Bi-section to fine the root of f(X)=X 2 -3 between X =1 and X=2. XM=(XL+XR)/2.

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Lecture 7

XM=(XL+XR)/2