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"ADH" <adoug48@xxxxxxxxxxx> writes:
>Problem: Let G= {a+b*sqrt(2)},where a and b are rational numbers not
>both 0. Prove that G is a group under ordinary multiplication.
In article <dcgfa3$pmh$1@xxxxxxxxxxxxxxxx>,
Lee Rudolph <lrudolph@xxxxxxxxx> wrote:
>I would say, start with the definitions.
Next step might be to try to generalize the problem and see what goes
wrong. Could you carry out the problem with the "sqrt(2)" replaced by
"sqrt(3)"? With "sqrt(4)"? With "2^(1/3)"? How about if the phrase
"not both zero" were deleted? Many times you can discover the true
essence of an idea by trying to "break" a problem, seeing what happens
when you try to construct a counterexample to the assertion or
something very like it.
dave
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