The main problem with this concept is that it doesn't work. Then again, none of the "proposals" for dividing by zero work, because none of them make any sense. Not in any BIG metaphysical sense; mathematics isn't like that. It fails along with all other proposals because of the nitty-gritty details.

The reason all these methods fail is that they can never give a field or even a ring. You can't have a field, because

0 = (1/0) * 0 = 1
in a field, and that doesn't make sense. That's why you cannot divide by zero in a field, no matter how hard you think you're trying. You can't have a ring, because
1/0 + 1 = (1 + 1*0)/0 = 1/0, so
1 = 0
You're guaranteed to get nonsense, no matter what.

But enough of generalities. Here are the specifics of why this 'un doesn't work.

The Narrator somehow omits mention of why e chooses to write

1/0 = 10000000000000000000...
and not
1/0 = 12345678901234567890...
Anything which requires arbitrary decisions is likely false. This is an arbitrary decision, and it leads us deep into the mud.

What are 2/0, 20/0 and 2000/0 in The Narrator's system?

2/0 = 20000... 20/0 = 20000... 2000/0 = 20000...
It follows, as day follows night, that 2/0=20/0=2000/0. After all, we write them down the same way. And yet 2/0*0=2, 20/0*0=20, 2000/0*0=2000. How do 3 equal numbers "remember" how to become the right one?

It gets worse. The Narrator claims that you can do arithmetic:

20^- * 30^- = 60^-
I read that as saying that 2000/0 * 3/0 = 6/0. Cool. Of course, since all these "division by zero" gizmos end up being equal, I suppose it's no big deal.

We "can" also perform all arithmetic operations. Can we really?

60^- / 30^- = (6/0)/(3/0) = 2 (due to cancellation, or plain operating on the "infinite digits representation"), but also
60^- / 30^- = 20^- (due to The Narrator's multiplication example).
We immediately conclude that 2=2/0. And, since 2/0=anything/0, we see that 2=anything/0. Similar reasoning shows that anything=anything/0 (just multiply by 1/0=10^-), and so we see that 2=anything, so anything = anything else.

This is SERIOUSLY COOL STUFF! I'll ask The Narrator for a \$100 loan, and return just \$2, because 2=anything, so 2=100! Tell hir what, I'll pay 50% interest, and return \$3! At that rate of interest, I'm sure e will be delighted to lend me another \$100!! WE'RE RICH!!!

That's the problem with nonsense: it doesn't work. Not because of THE BIGOTRY OF SELF-APPOINTED "PROFESSORS" OF MATHEMATICS TOO BUSY PRESERVING THEIR CUSHY FACULTY POSITIONS TO CARE ABOUT NEW MATH.. No, it doesn't work because it doesn't make sense.

I'll end with a challenge to the many zero divisors (I'm sure I've convinced few of them, and as we've seen 1=2, so if there's one zero divisor there are sure to be many more...). The "old math" which you disdain has some limited application in differential equations, analysis, algorithms, geometry, probability theory, and a few other fields. Bring one application of your favourite method of dividing by zero. You get to choose here! Pick any phenomenon, and demonstrate that your method is:

1. Consistent (i.e. free of contradiction);
2. Useful for modeling that phenomenom.

No, forget about fulfilling a+b. Pick which one you want to fulfill, and do that one.

You won't manage. It doesn't work.

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