1. ## subspace

hi
we have $\mathbb{E}=\left \{ (x,y)\in \mathbb{R}^{2};xy=0 \right \}$,i want to know if $\mathbb{E}$ is stable for addition.i also want to know some informations about stability in sets it's new for me.
thanks.

2. Originally Posted by Raoh
hi
we have $\mathbb{E}=\left \{ (x,y)\in \mathbb{R}^{2};xy=0 \right \}$,i want to know if $\mathbb{E}$ is stable for addition.i also want to know some informations about stability in sets it's new for me.
thanks.

What does being "stable for addition" for a set mean, anyway? Does it mean it is closed wrt addition? If so then it's simple: check what happens with (1,0) and (0,1).

Tonio

3. well for $X=(1,0)$ and $Y=(0,1)$ elements of $\mathbb{E}$,we have X+Y=(1,1) not element of $\mathbb{E}$,does this equivalent of saying that $\mathbb{E}$ is not stable for addition ?

4. Originally Posted by Raoh
well for $X=(1,0)$ and $Y=(0,1)$ elements of $\mathbb{E}$,we have X+Y=(1,1) not element of $\mathbb{E}$,does this equivalent of saying that $\mathbb{E}$ is not stable for addition ?
Ok, what part of "what does being stable for addition mean" you didn't understand??
I DO NOT KNOW what does being stable for addition mean: I said that if it is what ALLLL the rest of the world calls "closed under addition" then...etc.