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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



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: > > > Dan <dan.ms.ch...@gmail.com> wrote in news:43bcf4320c9a41e29eea > > > c91fe4e80...@ia3g2000vbb.googlegroups.com: > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > On Feb 5, 4:24 pm, Robin Chapman <R.J.Chap...@ex.ac.uk> wrote: > > > >> On 05/02/2013 14:08, Dan wrote: > > > > > > >> > On Feb 5, 3:45 pm, Robin Chapman <R.J.Chap...@ex.ac.uk> wrote: > > > >> >> On 05/02/2013 13:27, Dan wrote: > > > > > > >> >>> Does there always exist a subgroup H of G such that G = NH , and > > > >> >>> (H intersection N) = the identity element? > > > > > > >> > Can you provide an example? > > > > > > > Fun fact :If the set of possible answers is infinite , and person T (T > > > > stands for troll) claims to have one ,then person B cannot determine > > > > for sure using only yes or no questions . Each question is a function > > > > from the set of remaining answers to {Yes,No} . Provided that the set > > > > is infinite , either the inverse image to Yes or the inverse image of > > > > No is infinite . There exists a sequence of choices as answers of T > > > > such that the set of 'remaining valid answers' always remains > > > > infinite , thereby always giving the impression of knowledge of an > > > > answer , while ensuring for a fact that such an answer does not > > > > exist . > > > > > > That's an interesting alternative universe you've got there. Something > > > closer to reality would be that person T (T for teacher) doesn't want to > > > do your homework for you, but was helpful enough to tell you the right > > > answer, so that you wouldn't waste a lot of time looking for a proof > > > rather than a counterexample. I'm surprised you aren't more grateful. > > > > > > B. > > > > '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



