For (vector) x and (vector) y in l(sub)2, we define

||(Vector)x|| = sqrt(x(sub1)^@+x(sub2)^2+...), (vector)x(dot product)(vector) y = x1y1+x2y2+...

Why does the series x1y1+x2y2+... converge?

Question

For (vector) x and (vector) y in l(sub)2, we define

||(Vector)x|| = sqrt(x(sub1)^@+x(sub2)^2+...), (vector)x(dot product)(vector) y = x1y1+x2y2+...

Why does the series x1y1+x2y2+... converge?

terenzreignz · Answer

For $\large \vec x$ and $\large \vec y$ in $\large l_2$, we define$$\Large ||\vec x|| = \sqrt{(x_1)^2+(x_2)^2+...}$$$$\Large \vec x \cdot \vec y = x_1y_1+x_2y_2+...$$
Why does the series $\large x_1y_1 + x_2y_2...$ converge?

Still... I get the feeling that something's missing...

terenzreignz · Answer

Still though, I don't know what $\large l_2$ is... guess I'm more of a newbie than you are ^_^