Divide by zero, solved?

Lord Zentei · Post by **Lord Zentei** » 2006-12-07 11:35pm

BBC really needs stricter editorial standards for their mathematical and scientific news articles. And by that I don't mean some random geek, I mean they need actual professionals with credentials on their payroll.

Despite this, they are markedly less bad than the great majority of mainstream media - a fact which is all the more shocking. I still cringe at the recollection of a news article on CNN.com which discussed a paper on abiogenesis where it was postulated that certain types of clay could have formed the protective environment for early self-replicating molecules. CNN's take: "Science now shows that life was created from clay, just as faiths preach". Ugh.

Post by **fgalkin** » 2006-12-08 12:11am

Admiral Valdemar wrote: It is also telling of the lowering of journalistic standards within the BBC who have so far managed to report on pseudoscience, kill the award winning series Horizon with stupid dumbed down stories and make the most basic errors on stories. It's like they don't care anymore.

Oh, and maths isn't science, ergo, sucks.

Of course they don't care. You think reporters actually care about this shit? To them, its just a job, they're not going to go the extra mile to do research when they can do something else. "Journalistic integrity" is the biggest myth the press is trying to propagate.

Have a very nice day.
-fgalkin

Sriad · Post by **Sriad** » 2006-12-08 12:38am

Destructionator XIII wrote:This definition solves nothing, but I want to clarify a little that has been posted here, because I am a nitpicker, basically.
bilateralrope wrote:So what problems does this definition solve, that defining x/0 = infinity doesn't ?
Define x/0 = inf isn't really accurate. One could say that the limit as a approaches zero of x / a = infinity (which is very useful in calculus), but x / 0 on its own is still undefined.

The reason for the undefinition being that it can be +/- infinity, as is clear if you approach 0 via arbitrarily small negative numbers instead of positive. Or freaky complex infinities, if you want to get into that.

Winston Blake · Post by **Winston Blake** » 2006-12-08 01:18am

Lord Zentei wrote:Despite this, they are markedly less bad than the great majority of mainstream media - a fact which is all the more shocking. I still cringe at the recollection of a news article on CNN.com which discussed a paper on abiogenesis where it was postulated that certain types of clay could have formed the protective environment for early self-replicating molecules. CNN's take: "Science now shows that life was created from clay, just as faiths preach". Ugh.

Is it worse than this?

Post by **fgalkin** » 2006-12-08 01:30am

Yes. That's a simple mistake, someone typed in "light" instead of "sound" without thinking, and whoever's in charge of the broadcast missed it. The other one is pure sensationalism.

Have a very nice day.
-fgalkin

Post by **Darth Wong** » 2006-12-08 01:36am

The general fact that news has morphed into "newstainment" is far more damning than any particular example you can bring up.

Post by **fgalkin** » 2006-12-08 01:45am

Darth Wong wrote:The general fact that news has morphed into "newstainment" is far more damning than any particular example you can bring up.

Blame public education. Once you got the masses (barely) literate, you had to stoop to their level to make money.

Have a very nice day.
-fgalkin

Post by **Surlethe** » 2006-12-08 03:43am

Jesus Christ. I grew out of my "you can divide by zero" phase in the eighth grade.

Another way of looking at the problem with division by zero is considering a general ring. Then the zero of a ring R is its additive identity -- i.e., for all x in R, x + 0 = x. It's not difficult to show* that multiplication of any element by zero is zero.

Now, here's where the real problem arises: multiplication is a binary operation, and hence is a function from RxR back to R. Suppose that R is non-trivial, and there exists some element 0^(-1) such that 0*0^(-1) = 1. Then we would be able to map from the element (0, 0^(-1)) in RxR back to any point in R, quite literally breaking the binary operation.

Why anyone would take him seriously when he's presenting his results to high-schoolers is utterly beyond me; a high-schooler is certainly not capable of comprehending any mathematics near as abstract as this.

* Let a, x in R. Then a(x+0) = ax, and so a(0) = ax - ax = 0, and (x+0)a = xa implies 0(a) = xa - xa = 0.

EDIT: From the picture on the dry-erase board in the article, could he perhaps be talking about a compactification of the reals?

Kuroneko · Post by **Kuroneko** » 2006-12-08 06:55am

In the one-point compactification (analogous to stereographic projection), x/0 can be unambiguously equated with ∞ for any nonzero x. In the two-point compactification (affine extension), x/0 is no longer well-defined, but we can say |x/0| = +∞. In any case, it doesn't really matter. Introducing a new symbol Φ that follows some axioms is not in itself invalid, but pretending that it solves anything is another matter entirely. In the strict sense, it may be true, but at a cost to algebraic structure that makes it not just worthless, but not even interesting.

The idempotency Φ² = Φ is given by the same sort of argument that has 0^0 = 0^(1-1), now with 0^(2-2). One way one could extend it is to have (a,b)≡"a+bΦ", which gives (a,b)+(c,d) = (a+c,b+d) and (a,b)·(c,d) = (ac,ad+bc+bd). However, multiplicative inverses are actually entire lines in the 'nullity plane', which also means that any particular of these 'numbers' is a multiplicative inverse of infinitely many other numbers, so we can't even take a quotient space to give back uniqueness without collapsing everything.