[NBLUG/talk] OT division by zero OT

[Steve Zimmerman]

If you can't handle aggressive scientific argument, you may
not want to read this post.  Parental guidance suggested.
No deities worshipped.

"Zero cannot 'go into', i.e., be divided into any number; therefore,
division by zero is meaningless, hence undefined."  So goes the
argument, but the argument is erroneous.

Six times zero is zero.  Six zeroes is as meaningless as six divided
by zero, but the answer is still zero, because it's obvious
that six zeroes equal zero, just like six paychecks that say $0.00 equal
zero dollars.

Thus, any number divided by zero equals zero, because "nothing" goes
into "something" zero times.  If you can have six zeros equaling zero, then
it is equally logical to have zero zeros as the quotient of any real, non-zero
number divided by zero.  "Nothing" goes into "something" zero times.
There are zero "nothings" in "something.  There is one "nothing" in 
"nothing":  0 / 0 = 1.  (This last sentence is kind of semantically cool;
it's like saying, "How many symbols `0' comprise the symbol `0'?)

Using our (nblug's) idea of "unary arithmetic," we could say, "How many
`symbols for zero' go into 6?  What is the answer?  The answer is zero.
Then you could say, "Well, of course not, the Romans didn't have any
symbols for zero.  Ah, but my point is still valid.  Because we *do* have
the symbol for zero.  So I ask you:  In a unary number system like the
Roman numeral system, how many `symbols for zero' go into 6?  The 
answer is "none," zero.  As Eric pointed out, six symbols for 1 go into
six, even though five of them are abbreviated.  Hence, I can ask the
question, "In a unary number system like the Roman numeral system,
how many `symbols for zero' go into n, where n != 0?"  And the answer
will always be the same, zero.  Thus, division by zero is defined.

I reject the argument, "x amount of textbooks say that division by zero
is undefined, therefore division by zero is undefined."  The fact that x
amount of textbooks say that division by zero is undefined only proves
that x amount of textbooks say that division by zero is undefined.

These textbooks never once prove that division by zero is undefined;
they state the accepted convention that division by zero is undefined.
How could the statement, "Division by zero is undefined" be proven
anyway?  To say, "Division by zero is undefined" is like saying, "We've
nothing to say about division by zero."  It's an accepted convention
that some mathematicians have agreed upon: "We'll have nothing to 
say about division by zero."  Thus there is no proof that division by
zero is undefined, because if you don't have anything to say about 
division by zero, then you certainly aren't proving anything about 
division by zero, now, are you?

They're saying nothing; I'm saying something.  I'm saying that division
by zero is defined (by me), and that division by zero equals zero, 
for numerator != 0.

Disclaimer:  Intellectual argument is not threatening to me, it's like
intellectual handball: I've won a few with nblug folks, I've lost a few.
It's no big deal, and I don't take it terribly seriously.  It's like the 
title of Linus's book: _Just for Fun_.      :-)

Best wishes,

	-- Steve Zimmerman