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Anonymous
SCREEN FROM BOOK != FUCKING HOMEWORK 2016-11-01 07:09:09 Post No. 8448920
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SCREEN FROM BOOK != FUCKING HOMEWORK 2016-11-01 07:09:09 Post No. 8448920
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So anyway, I understand and can visualize how composition of shift and rotation would always have a fixed point, but how can it remain fixed, when you take a homothety of < 1 after that, unless of course you specifically choose it's center to be that fixed point?
I've seen some proof on stackexchange, but it included linear algebra which is obviously unacceptable, since it's a FUCKING ANALYSIS book - intro chapter of the first volume in fact - and you're clearly supposed to be able to solve it without linear algebra.
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>>8448920
Anglais, s'il vous plait
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>>8448920
>>8448982
Here you go, engbro
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>>8448920
had me up to > when you take a homothety of < 1
It's a linear algebra question...shift and rotation are linear operators.
What's the book name? chapter? question?
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f(z) = a z + b
f(z)=z
z = a z + b, where a,b and z are complex.
z = b/(1-a)
works except when a = 1. When a=1 and b [math]\ne[/math] 0, there is no fixed point. When a=1 and b=0, every point is a fixed point.
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>>8448984
It's obviously a contraction mapping. This is a straightforward application of the Banach fixed point theorem
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>>8450093
You Russians are supposed to be good at math, step it the fuck up
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>>8449218
Chapter is Sets, first introductory chapter even before reals.
So clearly you can avoid using complex numbers.
>>8450094
This is the first time I hear this.
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