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Which of the following sets are dense in $\mathbb R^2$ with respect to the usual topology.

  1. $\{ (x, y)\in\mathbb R^2 : x\in\mathbb N\}$

  2. $\{ (x, y)\in\mathbb R^2 : x+y\in\mathbb Q\}$

  3. $\{ (x, y)\in\mathbb R^2 : x^2 + y^2 = 5\}$

  4. $\{ (x, y)\in\mathbb R^2 : xy\neq 0\}$.

Any hint is welcome.

  • 0
    Do you mean "Which of the following are Dense in $\mathbb{R}^2$"?2012-06-11
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    I edited your question for formatting, and changed "dense in $R$" to "dense in $\mathbb R^2$". Is this correct?2012-06-11
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    Think about what those sets really are. For example 3. is a circle of radius $5$. Can that ever be dense? Similar considerations apply to 1. whereas 4. consists of all of $\mathbb{R}^2$ minus the coordinate axes, so clearly it's dense. etc, etc.2012-06-11
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    What do you think? Have you tried anything yet? It's often better to include any working you've already done when posting on here!2012-06-11
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    @AlexBecker: Thanks a lot.2012-06-11
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    @AlexBecker: I checked , it is R.2012-06-11

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