What is "general position" of hyperplanes? A brief question. I was reading some mathematical writing in which the author makes the following statement:

Consider $S$ hyperplanes in general position...  

What is "general position"? Googling does not return a satisfying answer. 
Note: I'm not exactly sure how to tag this, so please correct tags as necessary.
 A: Great question.  Let's first work in $\mathbb{R}^3$ with $2$-planes to develop intuition.
Suppose I have two $2$-planes in $\mathbb{R}^3$.  If I choose their orientation 'at random,' I will almost surely find that they intersect in a line.  It is only in the very rare case that the two planes are parallel that they won't intersect at all (Notice I am using probabilistic language here without defining a probability space, but we're just trying to develop intuition at the moment).  So, we say that two $2$-planes are in general position if they intersect in a line.
What if we have three $2$-planes?  Well, in that case, we still want each pair to be in general position, so each pair should intersect in a line, but there is another condition that we should impose as well.  Again, if I chose the orientations of the $2$-planes at random, it would be a surprise if the intersection of all three was the same line, or three different lines, as the following pictures show:
$\hspace{1.2in}$
Instead, we expect the three $2$-planes to intersect at a point.
Finally, with four $2$-planes, you can see that general position means that any two of them intersect in a line, and three of them intersect in a point, and the intersection of all four is empty.
See if you can generalize the above intuition to the following definition:

We say that $m$ hyperplanes in $\mathbb{R}^n$ are in general position if for $1\le k\le n$ any collection of $k$ of them intersect in an $n-k$-dimensional plane if $1\le k\le n$, and if $k>n$ any collection of $k$ of them have empty intersection.

Another way to view this condition is with normal vectors.  From this point of view, $m$ hyperplanes are in general position if any subset of $k$ normal vectors of the $m$ hyperplanes is linearly independent whenever $k\le n$.
