- #1

Yankel

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Hello all,

I am trying to determine if the domain of the function:

\[f(x,y)=\frac{\sqrt{ln(x^{2}+y^{2}+1)}}{\left | x \right |+\left | y \right |+\sqrt[4]{xy-1}}\]

Is an open set or closed set and if it's bounded.

The domain is in the attached graph.

View attachment 2468

The book say it is closed and unbounded. I wonder, how can it be closed, when it goes to infinity ?

I may be confusing boundary with open/close, but shouldn't it be open if it goes to infinity, or is it enough to say that since every point is interior it is closed ?

thanks !

Edit: What I mean is, isn't it like sets of 1 variables, were we always write [a,infinity) since infinity can't be closed ?

I am trying to determine if the domain of the function:

\[f(x,y)=\frac{\sqrt{ln(x^{2}+y^{2}+1)}}{\left | x \right |+\left | y \right |+\sqrt[4]{xy-1}}\]

Is an open set or closed set and if it's bounded.

The domain is in the attached graph.

View attachment 2468

The book say it is closed and unbounded. I wonder, how can it be closed, when it goes to infinity ?

I may be confusing boundary with open/close, but shouldn't it be open if it goes to infinity, or is it enough to say that since every point is interior it is closed ?

thanks !

Edit: What I mean is, isn't it like sets of 1 variables, were we always write [a,infinity) since infinity can't be closed ?

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