Re: injective polynomial f: k x k -> k

In article <432fa939$1@xxxxxxxxxxxxx>,
Elias Vicari <vicariel@xxxxxxxxxxx> wrote:

>Looking at the niveau lines of the graph, considered as a function R x R
>-> R, one as to be extremely unlucky if each of those hits a rational
>pair only once... I know it is indeed possible, but unlikely...

On the contrary: a "generic" smooth curve on R x R will not intersect Q x
Q at all; a "generic" smooth curve through one point of Q x Q will not
have any other points of Q x Q. After all, there are only countably many
points to avoid.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada




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