What's the difference between "$B_1(0)$ in ($\mathbb R^2$, $∥⋅∥_2$)" and "$B_1(0)$ in ($\mathbb R^2$, $∥⋅∥_1$)".
I'm asked to plot $B_1(0)$ in ($\mathbb R^2$, $∥⋅∥_1$).
I know that $B_1(0)$ = {$x \epsilon \mathbb R^n : ||x||=1$} But I don't really understand it.
So do I just draw a circle of center $(0,0)$ and radius $r=1$ in an orthonormal system ($O, i, j$)?
Please if anyone could show me a picture of it. Thank you
suppose $(x,y)\in B_1(0)$ in $(\mathbb R^2,||\cdot||_2)$. then $\sqrt{|x|^2+|y|^2}=1$ so simply $B_1(0)$ is the standard unit circle in $\mathbb R^2$
Now suppose $(x,y)\in B_1(0)$ in $(\mathbb R^2,||\cdot||_1)$. then $|x|+|y|=1$. So if we draw a picture it will look like this.