Question

Define \[\mathbb{R} ^{3}\]What do they mean by "define"?

Answer 1

They want you to explain what it is.

Answer 2

So, it is a set of real numbers...? What about the power 3?

Answer 3

its the set of all vectors:
\[(x_1,x_2,x_3)\]
such that:
\[x_i \in \mathbb R\]

Answer 4

I believe that it signifies a 3-dimensional space (hence the cube)

Answer 5

its just a fancy way of saying you have 3 dimensional vector, and each element of the vector is a real number.

Answer 6

oh okay. hmmm. so is it always a vecotr? or is it just for this case?

Answer 7

it depends on the context of the problem. i guess the most general name for it is "n-tuple" (i wonder if i spelled that right).

in this case it would be a "3-tuple"
If it was:
\[\mathbb R^n\], the objects in the set would be "n-tuples"

Answer 8

oh okay. thanks (: