I originally learned vectors as something with a magnitude and direction, which meant that a vector could be translated, moved along a coordinate system.
But, they are actually just an n-set of coordinates. I recently realized, doesn't a set of coordinates give more information than just a magnitude and direction? They also give information relative to the origin, so vectors shouldn't be able to translate through a coordinate system, right?
Also, I'm familiar with representing things like forces with vectors as something with a magnitude and direction. I don't conceptually understand how to use a set to represent forces and other vector quantities.