[moose07]

N-space

Are you diving down this little rabbit hole, perchance?

We can locate any point in a coordinate system by using pairs of numbers. 
In 2D geometry we need 2 numbers, and in 3D geometry we need 3 numbers to express a point.
 Most probably many people don't know beyond 3D how to express a point.
 If we want to express a point in 4 or 5 or higher dimensional space, what can we do? A quadruple of numbers 
2
4
3
1
(2,4,3,1), for example, is used to represent a point in a 4 dimensional space, and the same goes for higher dimensions. Thus we can represent 
n
n-tuple of numbers in an 
n
n-dimensional space. Mathematically, there are many rules and properties of vector in these kind of space, which we'll discuss in this wiki. 
But we should keep in mind that it is impossible till now to geometrically visualize any tuple of numbers out of 3 dimensional space.

[Darksheare]

The only rabbit hole for rabbits to go down.

[ArGee]

But we should keep in mind that it is impossible till now to geometrically visualize any tuple of numbers out of 3 dimensional space.

I don't know if this is part of the theory of n-dimensional space, but I think you need to live in n+1 dimensions to properly visualize a point in n dimensions. Since we live in 4 we can visualize 3 but we work very hard to visualize 4.