How can I draw the graph of |xy| <=0

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- Jun 14th 2013, 06:10 AMkastamonuDrawing a graph
How can I draw the graph of |xy| <=0

- Jun 14th 2013, 06:16 AMPlatoRe: Drawing a graph
- Jun 14th 2013, 07:46 AMHallsofIvyRe: Drawing a graph
So the graph is two intersecting straight lines.

- Jun 14th 2013, 09:27 PMMINOANMANRe: Drawing a graph
There is no way to graph this. It is wrong. The | xy| is > =0 for every x,y and not <0

- Jun 15th 2013, 03:39 AMPlatoRe: Drawing a graph
Why in the world would you post that?

$\displaystyle \{(x,y) : x = 0 \vee y = 0\}$ is the graph in $\displaystyle \mathbb{R}^2$

This is the union of the $\displaystyle x\text{-axis}~\&~y\text{-axis}~.$

$\displaystyle \{(x,y,z) : x = 0 \vee y = 0\}$ is the graph in $\displaystyle \mathbb{R}^3$

This is the union of the $\displaystyle xz\text{-plane}~\&~yz\text{-plane}~.$

There were two correct replies posted. Are you saying that both Prof Halls and I are mistaken? - Jun 15th 2013, 06:19 AMMINOANMANRe: Drawing a graph
the |x| is never negative as simple as such..........the rest is blabla

- Jun 15th 2013, 06:28 AMPlatoRe: Drawing a graph
- Jun 15th 2013, 07:32 AMHallsofIvyRe: Drawing a graph
You are the one who is "blabla"ing. You seem to have misread the question. The original question was about graphing $\displaystyle |xy|\le 0$, the set of points (x, y) such that xy is either negative

**or zero**. Yes, |xy| is never negative but it**is**0. The graph is the two axes- the x- axis on which y= 0 so |xy|= |x(0)|= 0 and the y-axis on which x= 0 so |xy|= |(0)y|= 0. - Jun 15th 2013, 10:08 AMMINOANMANRe: Drawing a graph
Yes, |xy| is never negative but it is 0.......which implies x=0 and y=0..................I agree.....

do not use the < 0 it is wrong............................................. ......

and be more polite......after all we just exchange here views and ideas....and if we disagree in some issues this is just another expression of the plurality of Mathematics... - Jun 15th 2013, 10:25 AMPlatoRe: Drawing a graph
Again, why would any mathematically literate person write that?

Now that is being as polite as this situation calls for.

Did you miss read the OP?

The OP was $\displaystyle |xy|\le 0$ not $\displaystyle |xy|<0$.

If it had been the latter, then we all would agree that no nonempty graph exists. - Jun 16th 2013, 10:58 PMkastamonuRe: Drawing a graph