Posted on 12/08/2006 12:20:06 PM PST by LibWhacker
Schoolchildren from Caversham have become the first to learn a brand new theory that dividing by zero is possible using a new number - 'nullity'. But the suggestion has left many mathematicians cold.
Dr James Anderson, from the University of Reading's computer science department, says his new theorem solves an extremely important problem - the problem of nothing.
"Imagine you're landing on an aeroplane and the automatic pilot's working," he suggests. "If it divides by zero and the computer stops working - you're in big trouble. If your heart pacemaker divides by zero, you're dead."
Computers simply cannot divide by zero. Try it on your calculator and you'll get an error message.
But Dr Anderson has come up with a theory that proposes a new number - 'nullity' - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity).
'Quite cool'
The theory of nullity is set to make all kinds of sums possible that, previously, scientists and computers couldn't work around.
"We've just solved a problem that hasn't been solved for twelve hundred years - and it's that easy," proclaims Dr Anderson having demonstrated his solution on a whiteboard at Highdown School, in Emmer Green.
"It was confusing at first, but I think I've got it. Just about," said one pupil.
"We're the first schoolkids to be able to do it - that's quite cool," added another.
Despite being a problem tackled by the famous mathematicians Newton and Pythagoras without success, it seems the Year 10 children at Highdown now know their nullity.
Yes and no. In exact terms, the dividend asymptotically approaches infinity (either positive or negative) as the denominator approaches zero. Asymptotically means it "never quite gets there".
In more concrete (and practical) terms, the answer is infinity, or at least a number large enough to respresent a ridiculously large value (which can still be positive or negative).
The issue comes up in computing because computers can only handle certain ranges of numbers, with the end points of those ranges determined by the size of the container the value is stored in. The programmer can protect against overflow by preemtively testing for too small values in the denominator and substituting a very large number in place of the actual calculation, or they can reactively catch the overflow error (using exception handling) and substitute afterward. Or, the programmer can allow the built-in exception handling to take care of the problem, which commonly causes the program to stop working altogether.
I have to admit, though, "nullity" is exactly the WRONG word for this value continuum, because "null" is nothing, and therefore "nullity" cannot be defined rationally to mean "anything".
BTW - If I have insulted your intelligence or experience with my explanation, I apologize. You sounded as though you might appreciate a fairly complete answer.
Not so. The result of that operation is 'undefined', not 'infinity' (whichever of the 'infinities' you mean).
Jack Bauer doesn't count to infinity, but his cell phone battery does carry an infinite charge.
Jack stops whatever it is before it reaches infinity.
Nullity is when you have no music playing in your head.
(nullity, melody?)
See #36 for brains.
Sucker. Born. Every. Minute.
In division you must have both existence and uniqueness in order for division to make sense (if you're trying to divide 8 pieces of pie amongst 4 people, you don't want to get 2 pieces each on Monday and 3 pieces each on Wednesday); i.e., when we write
a/b = c
we mean there exists a unique number c such that a = b*c.
But what if b = 0 and, for example, a = 5.
Is there a number c such that 5 = 0*c? No. It doesn't matter which number you plug in for c. You'll never get 5. So we don't have existence. BIG problem.
OTOH, what if a = 0? Then we want a unique c such that 0 = 0*c. But every c will work in this case. So we don't have uniqueness either. Therefore, division by zero is left undefined.
If you divide an integer by an integer in your computer program you will get an integer result. Integers represent positive and negative numbers. For a 32-bit integer this means a range of –2,147,483,648 to 2,147,483,647. Those values use every single one of the 32 bits. How are you going to now represent "nullity" with "an arbitrary value" that will be returned when you divide by zero?
i is for current. "A" is for amps.
LONG RESPONSE: That is exactly what I did when I encountered a Divide-by-zero error in some GPS code. The fix was to assume GPS was unavailable at that particular space-time instant, since the satellite positions resulted in a near-singular navigation matrix.
SHORT RESPONSE: If you're dividing by zero, the problem's probably buggered anyway.
Dividing by 0 yields a contradiction. Remember that any number divided by itself is 1. Now, 0 can be the numerator of a rational number - which of course designates 0. If 0 can also be the denominator, then 0/0 must = 1. In a sense we would be saying that nothing equals something, which is only true in government. I suspect that there is a whole lot more to the mathematics than is revealed in the story.
I was given that equation recently during an oral exam and a bench full of electronic test equipment, the professor told me to prove the equation to him using the lab equipment.
Nullity is when Republicans are the majority party in Congress.
(snare, kick drum & cymbals)
In fact, nullity and zero are now two more factors which exist for ANY number, even prime numbers. Because for any number, nullity*0= that number.
Except that multiplication is now no longer a one-to-one function, since nullity*0 yields an infinite number of answers.
Also, any number divided by nullity is zero, but that isn't so problematic...
I'm really not ready for the autopilot to be landing my plane, not just because someone might have programed it to divide by zero, but also because it isn't likely to notice the cow wandering across the runway.
"Approaching" means "gets close to." The arrow does not mean "equal."
True. I remember that much from circuit analysis...we did use i a lot. ;)
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