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Polynomial $P(x,y)$ with $\inf_{\mathbb{R}^2} P=0$, but without any point where $P=0$
How can I build example of polynomial $p(x,y)$ that does not reach its infimum?
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Can you find an example of a one-variable polynomial that doesn't reach its infimum? – Christopher A. Wong Jan 17 '13 at 21:32
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1That question was asked a couple of days ago. Maybe someone can find it? One possibility is $P(x,y)=(1-xy)^2 +x^2$. – Git Gud Jan 17 '13 at 21:32
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3Polynomial $P(x,y)$ with $\inf_{\mathbb{R}^2} P=0$, but without any point where $P=0$ gives a nice answer. – Brian M. Scott Jan 17 '13 at 21:32