1200-year-old problem 'easy' [dividing by zero]

BBC ^ | 12/8/06

[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.

[gb63]

Loved those TRS-80's. Give me!

[MosesKnows]

doesn't dividing by zero yield an infinite value?

Yes

Example.

Divide 1 by 1 and the answer is 1
Divide 1 by 1/10 and the answer is 10
Divide 1 by 1/100 and the answer is 100
Divide 1 by 1/1,000 and the answer is 1,000
Divide 1 by 1/10,000 and the answer is 10,000
Divide 1 by 1/100,000 and the answer is 100,000
Divide 1 by 1/1,000,000 and the answer is 1,000,000

This illustrates that as the absolute value of the denominator approaches zero the answer approaches infinity. 1/infinity is almost as close to zero as one can get. Therefore, dividing 1 by 1/infinity is infinity. I trust I won’t have to explain why I said “almost as close”.

[Right Wing Assault]

I would like to know who the first person was who died from his pacemaker dividing by zero.

[cynwoody]

Typical BBC empty filler.

This problem has been solved, and you are using the result right now.

http://www.gnu.org/software/libc/manual/html_node/Infinity-and-NaN.html

[RoyStevens]

Why is that?

[Slings and Arrows]

Even so.

[vrwc1]

Declare the pointer to the value to be null after exception handling the divide by zero error.

What does that have to do with the value of nullity?

Either that, or we determine that the lowest value for a given variable or its highest possible value (either –2,147,483,648 or 2,147,483,647 since we're using 32 bit signed integers) to be a divide by zero condition.

By "divide by zero condition" do you mean "nullity"? If that's the case, we have to do that for all types (signed and unsigned 8-bit, 16-bit, 32-bit, 64-bit integer values, floats, doubles, etc.). Now all of a sudden "nullity" is represented by many different values depending on the data type. That just doesn't make sense!

It doesn't fall on the number line, so it is impossible to represent using binary unless you special case the value, which is what you're doing in your code now to avoid divide by zero errors. So defining "nullity" doesn't help you at all in your programs. You're better off doing precondition checking to insure you don't divide by zero, or handling it after the fact by catching the exception.

[Hostage]

Dividing by zero makes any number equal to any other number. It renders the number system meaningless.

Suppose a=b:

a^2-b^2 = a^2-ab = a(a-b),

but

a^2-b^2 = (a+b)(a-b);

therefore,

a(a-b) = (a+b)(a-b)

and dividing by a-b we have

a = a+b.

Let a = 1. Then 1 = 1+1 = 2.

Isn't that special?

[Slings and Arrows]

*sniff* I miss my TI-99/4a!

[lepton]

I prefer PV=nrT

[2 Kool 2 Be 4-Gotten]

Yes, this guy is to mathematics as Rodney's Dr. Vinnie Goombatz is to medicine.

[Doc Savage]

Al Gore used it to predict the end of the world! See, it works!

[lepton]

And what is infinity/pi^2? :)

[YouPosting2Me]

"In the LIMIT!"

[Slings and Arrows]

And what is infinity/pi^2? :)

A jillion. Plus fifty cents.

[Alouette]

My favorite Integral is e^x

[Slings and Arrows]

I've always found e to be a bit irrational. *rimshot*

[AmishDude]

2+2=6 as 2 approaches 3.

[lepton]

A jillion. Plus fifty cents.

I think you forgot to carry the pineapple-upside-down-beans.

[JamesP81]

You're better off doing precondition checking to insure you don't divide by zero, or handling it after the fact by catching the exception.

That's pretty much what I just said.

Exception handling is usually all that's needed unless for some reason you need to retain the fact that you divided by zero later in the code. That's not too common, but not unheard of either.

If you do need to retain a divide by zero in memory, pointers in most programming languages help you out. In most languages, pointers can be set to null (with 'null' being a reserve word). I don't know what the binary code behind this is, but it doesn't matter. What matters is that I can set a pointer to null if I divide by zero, and that's a special case that works no matter what. Most languages that do this also overload the '=' operator so you can test if a pointer's value is null.

As for special casing based on data type, if I absolutely have to do that (and never have, at least not in my professional work that I can remember), I'll try to use the same length (8 bit, 16 bit, etc) for all my variables if memory permits. Not very efficient or clean but it can be done if you have to retain a divide by zero when the language you're using doesn't let you set a pointer equal to null. At least then you only need to set two special cases; one for integers and one for reals.