Undefined my ass!

Okay, this one has kept me up too many nights. Not because I can't figure it out, but because it is so unbelievably simple that it simply has to be true. I would invite you to invite all of your math friends to check this out for me.
0*0=0 right?
Infinity*infinity=infinity right?
X * infinity=infinity
X * 0 =0

Okay, that's the background. Now here's the deal. When you get into dividing numbers by zero, or dividing numbers by infinity, they say that the answer is 'undefined'.
Here's a quick (not really)explanation of why that is. (If you like you can skip the explanation and move to the next paragraph following the explanation)
THE EXPLANATION FOR WHY YOU CAN'T DIVIDE BY ZERO OR INFINITY
Because there's just no sensible way to define it.

For example, we could say that 1/0 = 5. But there's a rule in arithmetic that a(b/a) = b, and if 1/0 = 5, 0(1/0) = 0*5 = 0 doesn't work, so you could never use the rule. If you changed every rule to specifically say that it doesn't work for zero in the denominator, what's the point of making 1/0 = 5 in the first place? You can't use any rules on it.
But maybe you're thinking of saying that 1/0 = infinity. Well then, what's "infinity"? How does it work in all the other equations?
Does infinity - infinity = 0?
Does 1 + infinity = infinity?
If so, the associative rule doesn't work, since (a+b)+c = a+(b+c) will not always work:
1 + (infinity - infinity) = 1 + 0 = 1, but
(1 + infinity) - infinity = infinity - infinity = 0.
You can try to make up a good set of rules, but it always leads to nonsense, so to avoid all the trouble we just say that it doesn't make sense to divide by zero.
What happens if you add apples to oranges? It just doesn't make sense, so the easiest thing is just to say that it doesn't make sense, or, as a mathematician would say, "it is undefined."
Maybe that's the best way to look at it. When, in mathematics, you see a statement like "operation XYZ is undefined", you should translate it in your head to "operation XYZ doesn't make sense."

UNDEFINED MY ASS
This reminds me of the commercials where they try to pass off baffling legalese to children to rob them of their toys. The commercials end with "Even a child knows etc" I think even a child would realize that the above undefinition is a cop out.
I think my explanation, as follows, makes a lot more sense. My theory mathematically proves that nothing is everything, and everything is nothing. It proves that the universe is one giant singularity. Are you ready, it's not that complicated.
Imagine if you will, a number line. The negatives go off to the left to negative infinity, the numbers go off to the right to positive infinity. This is the same line we all learned in the 4th or 5th grade.
On the number line zero sits between 1 and -1. Infinity sits at either end of the number line.
What I'm going to ask you to imagine next is this: We don't count out to infinity in each direction. We count down to 0 from infinity in each direction. 0 isn't the start or beginning, it's the midpoint. It's the sum of all points. (-infinity)+(positive infinity)= 0. In this instance, because the range of points from 0 to infinity = infinity, and the range of points from 0 to -infinity is infinity, we can see that 0, being the exact halfway point could be expressed as infinity/2=0. Consequently, 0*2=infinity. These equations work IF 0=Infinity.
Do you get it? Yeah, that just happened to your head. So what can I do with this now?