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Topic: Ask-an-Analysis problem
Replies: 10   Last Post: Apr 25, 2013 1:01 PM

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David C. Ullrich

Posts: 3,531
Registered: 12/13/04
Re: Ask-an-Analysis problem
Posted: Apr 25, 2013 10:44 AM
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On Wed, 24 Apr 2013 19:06:20 -0700, William Elliot <marsh@panix.com>

>On Wed, 24 Apr 2013, dullrich@sprynet.com wrote:

>> >Assume for f:[0,1] -> R that there's some c /= 0,1 with
>> >for all x in [0,1/2], f(x) = c.f(2x).
>> >
>> >Show there's some k with for all x in [0,1], f(x) = kx.

>Whoops, indeed a hypothesis was omitted.
>Assume for continuous f:[0,1] -> R here's some c /= 0,1 with
>for all x in [0,1/2], f(x) = c.f(2x).
>Show there's some k with for all x in [0,1], f(x) = kx.

As has been pointed out several times already, there
are trivial counterexamples, like f(x) = x^2.

>> Forget what I said this morning. The question was either
>> totally garbled or totally stupid to begin with.
>> f(x) = x^2 is a counterexample.

>You could go to Ask-an-Algebraist forum at
> at.yorku.ca/topology
>to give your simple disproof directly to the primary source.

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