This is in fact very easy when you think of the linguistics of the idea instead of mathematics. This is why I won't be using any equations, inequalities, or anything like that in my arguement. Existing maths don't allow dividing by 0, so of course any mathematical representation wouldn't work.
Here's the thing: Division of x/y is taking x and putting it into y parts. 8/2 is taking 8 (lets say apples) and putting them into 2 groups. We've all done this as kids:
@ @ @
@ @ @
Those are our apples. If we put those into two groups, we have this:
@ @ @ @
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Each group has four apples. 8/2=4 (ok, maybe I lied about no equations).
Now, if we do 8/0, we specify no groups. If there are no groups of apples, of course you have no apples! If we were to say "parts" instead of "groups," you could look at the saying "I'll have no part in this."
If this person is having no part in this:
"this" / "no part" (just go along with me)
Then they are not involved with "this" at all. There is no "this" in the person's life. Saying that a person will have no part in something does not mean that this person will have an undefined part in said activity!
For the record, I truly hope that someone can prove me wrong beyond any doubt, because if I was right, it would be too hard to convince anyone.
Looking back on this half-decade old writeup (it is now September, 2006), I realize how ridiculous I was being.
In my original, rambling writeup, I claimed that if you take eight apples, put them in no groups, well, then you have no apples! Never did I touch on the feasibility of putting them in no groups. There is always going to be a group. In the case of my old writeup, that group is the group of apples that I am not considering.
So instead of no apples, I really have two groups. The empty group of apples that I want to think about (this is the only group I thought of originally), and the group of eight apples that I would like to conveniently ignore. Unfortunately, ignorance is not good math.