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1200-year-old problem 'easy' [dividing by zero]
BBC ^ | 12/8/06

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.


TOPICS: Culture/Society; United Kingdom
KEYWORDS: anderson; dividing; easy; education; iaresmart; piledhigheranddeeper; publickskool; pythagoras; zero
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To: mountainlyons
This is the kind of stuff that you get when you do not teach because you do not want to hurt someones feelings.

No, it's the result you get when people work with real numbers in computers instead of theory on a chalk board. Try computing the cos of Latitude when you're on the equator. That's a very real problem, and if you forget to handle the exception and someone flies your autopilot across the equator and the GPS hits it just right, someone could die.

It'd be much better if the hardware just delt with it, and by naming this thing he justifies changing the hardware.

181 posted on 12/08/2006 2:01:12 PM PST by narby
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To: narby
Yeah. It's semantics. But words do mean things.

So if words to mean things, why does infinity need another name? Infinity isn't good enough - we have to call it nullity now?

The largest value possible for the variable type you're using. It will not be an exact value, but there are quite a few irrational numbers in this business, and "close enough" is the norm.

That doesn't help you any. See post #127 for an explanation. Besides, if that's what you want to do, why do you need the concept of nullity? All you really need is a compiler that will return MAX_INT when you divide by zero. You can do that yourself with exception handling or precondition checking. Nullity doesn't bring anything new to the table.

182 posted on 12/08/2006 2:01:31 PM PST by vrwc1
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To: narby
Computers handle variables whose values span extremely large ranges with a type of representation called floating point.

One problem was that every designer of a computer or computer language tended to "roll their own," resulting in calculations and variable transfers that were inconsistent across computers, and which sometimes had hidden flaws in their algorithms, as well.

[Recall that an early Pentium had a flaw in one of its trig/floating point instructions, and had to be recalled.]

Twenty years ago or so, computer/software engineers and applied mathemeticians began work to standardize floating-point representations and algorithm across all platforms, under the aegis of the Institute of Electrical and Electronics Engineers.

They devised special representations which would stand for unrepresentable quantities such as "infinity" and "Not-A-Number," (NAN), typically the result of a division by zero.

If you were doing a chain of calculations and somewhere along the chain the quantity would become unrepresentable, it would come out as NAN, which would be propagated throughout the remainder of your calculation.

Anybody using a standard IEEE-754 properly will get both exception conditions which can interrupt his normal processing flow, and NANs or infinities as values, both of which can keep the program from doing stupid or destructive things.

If the programmer knows what they're doing! < }B^)

183 posted on 12/08/2006 2:01:33 PM PST by Erasmus (Go to Sebastopol and Crimea River.)
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To: Stone Mountain
You mean a rational result, right? 2 divided by 3 does not yield an integer.

Depends on the language and the types of variables used. For true integer division in the "C" family of languages, 2 divided by 3 is 0, with a modulus of 2. Using floating-point math, 2 divided by 3 is 0.6666... (to whatever resoltion the storage variable keeps).

184 posted on 12/08/2006 2:02:52 PM PST by kevkrom (WARNING: The above post may contain sarcasm... if unsure, please remember to use all precautions)
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To: Ken522

Umm, the logarithm of the divisor, zero, is also an undefined number.


185 posted on 12/08/2006 2:03:35 PM PST by Erasmus (Go to Sebastopol and Crimea River.)
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To: LibWhacker
See my comment #145. He's not just dumbing down his poor students a little bit, he's making them truly stupid.

I disagree. It seems to me he's introducing them to a truly interesting concept of math. He hasn't introduced a "proof" that it's possible to divide by zero. It seems more that he has devised a convention for an algorithm to decide what to do in the case where a number is divided by zero.
186 posted on 12/08/2006 2:04:05 PM PST by Stone Mountain
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To: LibWhacker

I have only one question for this guy.
5 divide by nullity is what?


187 posted on 12/08/2006 2:05:21 PM PST by Boiler Plate (Mom always said why be difficult, when with just a little more effort you can be impossible.)
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To: JamesP81

Yeah, whatchoo said.

< }B^)


188 posted on 12/08/2006 2:06:30 PM PST by Erasmus (Go to Sebastopol and Crimea River.)
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To: LibWhacker

This will be useful about the time I retire when Social Security goes bankrupt. Amazing!


189 posted on 12/08/2006 2:06:37 PM PST by chesley (Liberals....what's not to loathe.)
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To: 2banana

To get a woman it takes Time and Money:

Women = Time x Money

And Time is Money and Money is Time

So: Women = Money x Money = Money^2

And Money is the root of all Evil

Money = SQRT(Evil)

So: Women = (SQRT(Evil))2

Or

Women = Evil (mathematically proven)

Since (SQRT(x)) is a real value only only when x>0, Women=Evil only when you have real money. When you don't, women are imaginary.


190 posted on 12/08/2006 2:06:49 PM PST by dangus (Pope calls Islam violent; Millions of Moslems demonstrate)
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To: Stone Mountain
You mean a rational result, right? 2 divided by 3 does not yield an integer.

No, in a computer program you will get an integer result. If you are assigning the result of (2/3) to an integer, you will get an integer result of 0.

191 posted on 12/08/2006 2:08:31 PM PST by vrwc1
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To: GYPSY286
I asked her if I had an apple in my hand and she multiplied it by 0, would it not be 1 since I still held the apple?

I would say no. Multiplying by zero would be the equivalent of losing the apple. If you multiply by two, you have two apples. If you multiply by zero, you have zero apples.
192 posted on 12/08/2006 2:08:51 PM PST by Stone Mountain
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To: vrwc1
So if words to mean things, why does infinity need another name?

To give an excuse for the computer hardware people to change how it works.

Besides, if that's what you want to do, why do you need the concept of nullity? All you really need is a compiler that will return MAX_INT when you divide by zero.

MAX_INT? Not a very big number to represent infinity.

If it was the compiler that was doing the testing, then I might as well put the code in myself. I'm trying to avoid machine cycles by getting this kind of thing into hardware.

193 posted on 12/08/2006 2:10:21 PM PST by narby
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To: vrwc1
You mean a rational result, right? 2 divided by 3 does not yield an integer.

2 divided by 3 does not yield an integer.

No, in a computer program you will get an integer result.

I don't understand. Are you talking about a program that rounds to the nearest integer? Most computer programs that I know (computers, calculators) will not yield an integer when dividing 2 by 3.

I suspect I'm missing something here. What is it?

194 posted on 12/08/2006 2:11:42 PM PST by Stone Mountain
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To: JamesP81
No. Not backing away from it. It's just another possible way of dealing with it. Your earlier question suggested me that you were wanting to know how to store a divide by zero result in memory. That's where the arbitrary value and null value ideas come into play. They aren't the only methods of dealing with it.

As I've said, exception handling is normally sufficient.

So since there are so many ways of dealing with the divide by zero problem in a computer program, the concept of "nullity" isn't really useful to programmers, right?

195 posted on 12/08/2006 2:11:43 PM PST by vrwc1
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To: LibWhacker

Would help with spreadsheets. Instead of getting an ERR (e.g., percent growth from zero), a simple symbol would look nicer.

Other than that, for other real-world applications, I maintain that reasonable approximations are sufficient, such as from a cost/benefit standpoint.


196 posted on 12/08/2006 2:11:56 PM PST by P.O.E.
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To: kevkrom
in the "C" family of languages,

Aha - knew I was missing something - thanks!
197 posted on 12/08/2006 2:13:44 PM PST by Stone Mountain
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To: P.O.E.
Symbol for nullity (bottom).

Or how about this one:


198 posted on 12/08/2006 2:15:16 PM PST by P.O.E.
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To: narby
MAX_INT? Not a very big number to represent infinity.

But in your previous post you said "The largest value possible for the variable type you're using." That's what MAX_INT is for integer types!

I'm trying to avoid machine cycles by getting this kind of thing into hardware.

I'm don't see how the concept of "nullity" does that.

199 posted on 12/08/2006 2:15:57 PM PST by vrwc1
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To: LibWhacker
Being in construction most of my life, geometry is about as complicated as math has ever gotten.

That said, maybe someone can explain this to me. If zero indicates nothing, and you divide something by nothing, how are you dividing it at all? Aren't you simply left with "something"?

I understand about multiplying by zero because, you get the same product regardless of the order of the numbers (AxB = BxA).

What can I say, I'm the product of public schools.

And, I'm old. 8-)

Regards

200 posted on 12/08/2006 2:17:40 PM PST by Tinman (Yankee by birth, Texan by Choice..."Support the Troops" shouldn't be just a bumper sticker)
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