- #1

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I was told that on

**R**

^{2}, the inequalities

(1) [tex]x > 0, y > 0[/tex]

Is open and unbounded

(2) [tex]x \geq 0, y \geq 0[/tex]

Is

**closed**and unbounded

But this doesn't make sense to me. how could this be closed and unbounded? Clearly, x and y will never reach any finite value.

A boundary region is which one that doesn't stretch to infinity in anyway, but a closed region is one where it contains it boundary. [tex]x \geq 0, y \geq 0[/tex] goes to infinity, so it isn't bounded, but how does this "contain" infinity?