The answer appears below. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P(x, y) = x^2 + (xy + 1)^2 This is clearly nonnegative, and can be made arbitrarily small by letting x -> 0, y = -1/x. Since y can't be infinite, P(x, y) can't be zero. On Thu, Jul 12, 2012 at 8:57 PM, Mike Stay <metaweta@gmail.com> wrote:
On Thu, Jul 12, 2012 at 7:53 PM, David Wilson <davidwwilson@comcast.net> wrote:
image means what?
The values that are actually outputs of the function. http://en.wikipedia.org/wiki/Image_(mathematics)
On 7/9/2012 9:52 PM, Mike Stay wrote:
On Mon, Jul 9, 2012 at 6:51 PM, Mike Stay <metaweta@gmail.com> wrote:
On Mon, Jul 9, 2012 at 6:50 PM, Mike Stay <metaweta@gmail.com> wrote:
Is there a multivariate polynomial whose image over R^n is strictly positive?
Sorry, "strictly the positive reals".
Or better: "exactly the strictly positive reals."
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com