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Topic: Let G be a group , N a normal subgroup of G
Replies: 13   Last Post: Feb 6, 2013 6:11 AM

 Messages: [ Previous | Next ]
 Paul Posts: 780 Registered: 7/12/10
Re: Yes
Posted: Feb 5, 2013 1:43 PM

On Tuesday, February 5, 2013 6:03:06 PM UTC, Dan wrote:
> On Feb 5, 6:34 pm, Bart Goddard <goddar...@netscape.net> wrote:
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> > Dan <dan.ms.ch...@gmail.com> wrote in news:43bcf432-0c9a-41e2-9eea-
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> > > On Feb 5, 4:24 pm, Robin Chapman <R.J.Chap...@ex.ac.uk> wrote:
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> > >> On 05/02/2013 14:08, Dan wrote:
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> > >> > On Feb 5, 3:45 pm, Robin Chapman <R.J.Chap...@ex.ac.uk> wrote:
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> > >> >> On 05/02/2013 13:27, Dan wrote:
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> > >> >>> Does there always exist a subgroup H of G such that G = NH , and
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> > >> >>> (H intersection N) = the identity element?
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> > >> > Can you provide an example?
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> > > Fun fact :If the set of possible answers is infinite , and person T (T
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> > > stands for troll) claims to have one ,then person B cannot determine
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> > > for sure using only yes or no questions . Each question is a function
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> > > from the set of remaining answers to {Yes,No} . Provided that the set
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> > > is infinite , either the inverse image to Yes or the inverse image of
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> > > No is infinite . There exists a sequence of choices as answers of T
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> > > such that the set of 'remaining valid answers' always remains
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> > > infinite , thereby always giving the impression of knowledge of an
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> > > answer ,  while ensuring for a fact that such an answer does not
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> > > exist .
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> > That's an interesting alternative universe you've got there.  Something
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> > closer to reality would be that person T (T for teacher) doesn't want to
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> > do your homework for you, but was helpful enough to tell you the right
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> > answer, so that you wouldn't waste a lot of time looking for a proof
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> > rather than a counter-example.  I'm surprised you aren't more grateful.
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> > B.
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> 'Z4' is two characters that would have been a sufficient answer .

The answer 'No' is not necesarily less helpful than the answer Z4. The ideal is for you to come up with your own counterexample(s).
There is clearly such a thing of "too much help" in maths education. Z4 gives more help than "No" but that doesn't say which of the two answers is better.

Paul