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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>
wrote:
>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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