Dividing by Zero

Dear sci/math,

I have a problem i would like to understand. Everybody knows you can't divide by zero, like everybody knows that binary codes just consist of 0 and 1.
First question: Why do you take a variable that is not defined at
for such an important system?

Second question: Would there be any difference if zero was defined for the casual use of Computers?

Maybe someone can help me just imagining how zero could be defined a little, if my questions make too little sense.

Thanks anon.

Sorry for the mistakes, english is not my native language, i postet via phone and its pretty late here.

I don't understand your second question.  As for the first, what do you suppose you would define it to be?  Maddox once wrote something on this very topic.

"The quotient 5/0 or -9/0 was not included because it is impossible to make sense out of these symbols. Imagine trying to divide something into nothing, and you'll see why."

i thought that in binary codes, they just use the number 0 and 1 without it having any meaning. they could also take 5 and 9, but then people would ask "why 5 and 9" lol.

Look how far we've gotten with imaginary numbers. Why don't we start our own branch of mathematics based on dividing by zero?

>>4
It can simplify some things to use 0 and 1.  For example, logical AND can be defined as multiplication.

>>5
So try it.  I remember this guy Anderson invented the so-called transreal numbers where you could divide by zero.

What you must remember is hat all binary is is a simple Boolean logic system where 0 is off and 1 is on.

>>5
>>6
I remember reading the BBC article on James Anderson and specifically the "nullity" concept to come out of his transreal arithmetic.  It's been a long while, but I remember the impression I got after reading a little further than the article was that Anderson's theory got a lot of undeserved hostility simply because the BBC did a terrible job presenting it.  (This is unfortunately bound to happen every so often when reporters attempt to cover subjects they have no background in.)  It's not really suggesting division by zero is possible, it is just alternative way of having a computer handle the division by zero problem.

"Zero" is usually used to mean the additive identity of a ring (an algebraic structure with addition, subtraction, and multiplication, but not necessarily division, ahd the operations must satisfy some familiar requirements), and in this context division by it is only possible if the ring is trivial.  (If 0 is the only element, then of course you can say 0/0 = 0 without any problems.)

For any a in a given ring, a + 0 = a.  Multiplying both sides by a gives a(a + 0) = a*a.  Distributivity of multiplication over addition gives a*a + a*0 = a*a (= a*a + 0).  Subtracting a*a from both sides gives a*0 = 0.  In particular 0*0 = 0
If 0 has a multiplicative inverse, call it 0' (0*0' = 1), then 0*0*0' = 0*0', which yields (0 =) 0*1 = 1.  Then for a an arbitrary element of the ring, multiplying both sides of the previous equation by a gives (0 =) a*0 = a*1 (= a), so in fact the only element of this ring is 0.

The upshot is that division by zero isn't really possible unless you're not using a conventional notion of zero (or unless 0 is your only element).  Some people say wheel theory allows division by zero, and to be honest I haven't looked that far into it, but it's always looked to me like wheel theory has defined a new operation and simply labeled it as "division by zero" without it actually being directly related.

>>8
I browsed his treatise and had a similar reaction, but he didn't convince me that it was gainful thing to do.  I mean, one of the best things about the real numbers is that they are a field.  But his transreal numbers aren't, nor a ring, nor even a group.  The elements he added to the reals do not have additive or multiplicative inverses.

It is possible if you think of infinity as being a point, and a line as a circle passing through infinity.

It just destroys all information about the argument, and also you cannot use indeterminate forms such as 0/0, 0*∞, or ∞/∞ (also 0^0 but we are mainly considering multiplication and division.)

you can also consider infinity to be the Point at Infinity from projective geometry. In this case, you assign many infinities with angles. Now, you cannot divide by zero, unless you also assigning a direction to the zero.

points of division by zero in complex analysis are called poles, and roots are when it equals zero. both are singularities in similar ways.

>>3
The number 0 don't make sense. Imagine nothing, and you'll see why.

>>11
empty bag of apples

nothing is paradoxical after labeling nothing as nothing it begins to be something ergo no longer nothing.

Well, the use of the binary system started with perforated cards were a 0 would mean there was no hole and a 1 would mean there it a hole in the card.

>>13
Well that's why we actually call it zero, not nothing.  The empty set, or no solution, is more what you want if what you want is nothing.

>>16
What of an empty set, or ``bag'' if you will, of zeroes?

>>17
Like when I buy doughnuts.  I have purchased a bag of holes, and the doughnuts are merely defining the boundry of those holes.

The number zero comes from the arabic number sys.
Therefore you must remember that when speaking of zero the guy who translated had no understanding of what it could be (is there a Roman numeral zero?).
Point: Classic western/European culture still sticks and cannot understand zero is perfect balance and not nothing.
You have to unbalance the zero and division doesn't allow this. (perfection divides into perfection or sum-such nonsense if you will).

What about the fraction 0/0 compared to 0/1? .... There's the crux of it.

Zero, the empty set, null are all the same things conceptually.  They represent the absence of something.  Practical difference is the context in which they're used.