Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
David C. Ullrich

Posts: 2,752
Registered: 12/13/04
Re: Ask-an-Analysis problem
Posted: Apr 25, 2013 10:44 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.
>





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.