Nullity: New Math for Dividing by Zero.

From the website:

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." ...

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.

Link - via Slashdot

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I've always thought of the "Error: Divide by 0" message me calculator gives me as more of a philosophical statement than a mathematical one. Like "If a tree falls in the forest and no one is around to hear it, does it make a sound?" Going back to kindergarten, if there are seven apples, and no one is around to eat them, it doesn't matter how many there are. There could be millions, or one. So the answer to a divide by zero problem should be a variable. Am I making sense, or am I just rambling? I dunno, I'm not a math-y person...
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Division by zero is absurd, but triviality is quite useful.

There are 3 existential types, not just 2.

1) That which exists.

2) That which does not exist.

3) That for which existence is indeterminate.

Any trivial is of the third type because “The Existence of a Trivial is Indeterminate”.

This last statement can be proved quite easily. It says that given any unique object, there is no way to determine if the object is really itself, or if it is in fact a trivial clone of itself. This is indeterminate.

One can exploit this existential indeterminacy of the trivials to make all kinds of unusual models.

I think that Dr Anderson was on the right track, but he missed it. He claims to have invented a non-number, a nullity, but he should really be looking at triviality instead.

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