Is a vector continuous?

[frootloopers]

Can one consider the point [3,3] to be an element of the vector [2,2]?

 

[Deleted member 4993]

Can one consider the point [3,3] to be an element of the vector [2,2]?

What do you think?

Why do you think so?

How would define "an element of the vector"?

 

[Dr.Peterson]

Possibly you are confusing the concepts of "vector" and "ray". What is your definition of "vector"?

 

[HallsofIvy]

You seem to be confusing two different notations. I would have used "(2, 2)" to indicate a point. Further, [3, 3] indicates a vector that, if it were placed in "standard position", with its tail at the origin, would extend to the point (3, 3). However, a vector is "movable". A vector extending from (1, 2) to (4. 5) would be identical to "[3, 3]". In general, vectors do not "contain" points.