# Math Help - subspace

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.

Tonio

5. Raoh, this is YOUR problem. You used the term "stable under addition" which is not standard (English) so YOU are going to look in your text book or ask your teacher. Tonio asked what "stable under addition" meant and you responded by asking HIM, "Does it mean" and then gave, effectively, what in English would be called "closed under addition". I suspect that is correct, but I am afraid no one here can help you until YOU have checked the definition of "stable under addition".

6. well i translated from the French,anyway thanks for your help(both ).