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

Question

anonymous · Answer

They want you to explain what it is.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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"

anonymous · Answer

oh okay. thanks (: