Solve for subpart bI need typed answer , handwritten answer will get down vote. Let U be a non-principal ultrafilter over w. Suppose (r, :n 0, {n

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Let U be a non-principal ultrafilter over w. Suppose (r, :n 0, {n

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 20CR: Let T be a linear transformation from R3 into R such that T(1,1,1)=1, T(1,1,0)=2 and T(1,0,0)=3....

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Solve for subpart b I need typed answer , handwritten answer will get down vote.

Let U be a non-principal ultrafilter over w. Suppose (r, :n<w) is a sequence of real
numbers. We say that r is the U-limit of (n : n <w) and write U lim e, = r iff for
every e> 0, {n <w: l, - | <e} €U.
Show the following.
(a) If lim a, r, then limr,
(b) If lim.r,
a and 4 lim a
6, then a

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