Today I just realised something. For a dimension to truly be a dimension it needs to be perpendicular to all other dimensions. E.g. In 2 dimensions the x coordinate system is perpendicular to the y dimension. In 3 dimensions the z axis is perpendicular to both the x and y axis. Therefore it's not possible to have a system with dimensions greater than 3 because if you add another there's no way for it to be perpendicular to all three other axises. Now where is my Nobel award?
It can be perpendicular with a dimension greater than 3 based on the scalar product you defined.
If P and Q are vectors of a n-dimensional space :
P _|_ Q \equiv <P,Q> = 0 \equiv (P,Q) = Arcos<P,Q>/(Norm(Q)*Norm(P)) = Pi/2
I'm going to pretend you're not a retard and replace the ill-defined "x axis" with any spatial dimension.
If it wasn't perpendicular you could point out to me the direction of time in space, since you can't it's perpendicular to all axes.
Is the electromagnetic spectrum of energy also a dimension?
You probably couldn't say radio
Waves are distinct from microwaves though since they could potentially influence each other's dimension
If OP doesn't know the answer to his question, he most certainly doesn't understand anything from your explanation, and you know this.
So basically, you're just showing off your big boy knowledge by copying a definition from your textbook. What does that make you?
Right, a faggot.