Proper notation for writing all points in the 1st and 3rd cartesian quadrant?

[PhillipKP]

Homework Statement

What is the proper notation for writing the set of all ordered pairs of real numbers that are in quadrant 1 and 3 of the real plane?

Homework Equations

The Attempt at a Solution

I was thinking something like

$$\left\{ \left(x_{1},x_{2}\right)\in\mathbb{R}\,:\, x_{1},x_{2}\geq0\right\} +\left\{ \left(x_{1},x_{2}\right)\in\mathbb{R}\,:\, x_{1},x_{2}\leq0\right\}$$

Is this fine or will including the + operation mean I am including points in the 2nd and 4th quadrant?

 

[Mark44]

Since you're working with sets, you would want "union" rather than "plus."

 

[Elucidus]

Note: points in quadrants are not on axes and vice-versa, so you need to be careful with the use of >= and >.

It is also possible to describe the 1st and 3rd quadrants as

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

If you wish to include the axes, change the inequality to xy <= 0.

--Elucidus

 

[PhillipKP]

Thanks for the quick replies.

 

[Elucidus]

ERROR!

1st and 3rd should be xy > 0. The coordinates must be of the same sign.

Sorry, somehow I was thinking 2nd and 4th (sheesh, I feel silly).

--Elucidus

 

[PhillipKP]

No worries I figured it was a typo :)

Thank you for your time.