"The quantity formerly known as nullity."
Cheers!
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.
You can also think of the Dirac delta function as the derivative of the Heaviside step function.
Extra credit: can someone from the class explain the Kronecker delta? ;-)
Cheers!
Sometimes you can finagle your way around it by overdetermining the problem, e.g. quaternions instead of spherical polar coordinates.
Cheers!
Aptly named, in this macabre instance.
Thunderous applause!
As a machine-learning guy, AI-guy, and all-around messer-about with matrices, I know in my heart that introducing extra dimensions will result in my going straight to Hell. ;^)
"The quantity formerly known as nullity."
Cheers!
You're now in esteemed company.
In general it's used to annihilate off diagonal elements in a double sum.
ie
dijxixj = xixi
drjairxi = aijxi
The emoticon indicated I was just joshing.
Cheers!
You might want to check your algebra. (Your point is still valid. )
a^x = exp(x*log_e(a))...
try it...
>> x = randn;a=randn; a^x - exp(x*log(a))
ans =
0
(Matlab is perfectly happy with complex arithmetic. 'log' means 'log_e', 'log10' is log_10. Excel doesn't do complex arithmetic, but 'LOG' means 'LOG10', unless you enter a second argument, specifying the radix. 'LN' is 'log_e' to Excel. Excel also thinks that 1900 was leap year and 2100 wouldn't be, making them inconsistent with any known calendar, except the Excel calendar.)
The meaning of "Limit x -->0 [f(x)] = 1 " is that you can name any number you want, except zero, call it 'eta', no matter how small you make eta, I name a value of x, 'epsilon', such that a^epsilon < 1+eta and that as eta gets smaller, epislon also gets smaller.
Less than nothing, I've heard of that.
actually, he does not. merely a person who thinks outside the box, unlike yourself.
"Only Chuck Norris can divide by zero. Plus, Chuck Norris has counted to infinity.....twice."
Dick Cheney can divide i by 0. He respects Chuck Norris, but finds his mathematical abilities wanting.
It took my teacher nearly 15 minutes to realize that I had trisected the "straight line" from one end of the arc to the other, rather than the arc itself.
I suspect this "nullity" issue is similar, especially since the students seem to "almost" get it.
If you have some spare time, could you square the circle and invent a perpetual motion machine?
Sometimes called "Euler's equation" it contains the five most important numbers in analyis in a single equation, with no others introduced. Truly a thing of beauty. I "discovered" it independently, about a page before my calculus text blew the game.
Maybe Anderson is onto something. If your pacemaker stops you will end up outside the conventional number line, in nullity.
"If your heart pacemaker divides by zero, you're dead."
Only if the moron who wrote the program didn't put in an error catching sub-routine.
Dick Cheney never forgets an onerror module in his programs.
>>>Don't see it as anymore ridiculous than i. Square root of negative -1. What sort of math is that? <<<
Imaginary numbers (also called "Complex Numbers") are not really "imaginary". Areas of usage include quantum mechanics, electrical engineering, optics, chemistry, and fluid mechanics. They are also used in some economics calculations.
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