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## Main Question or Discussion Point

http://arxiv.org/abs/0907.1090" [Broken]

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http://arxiv.org/abs/0907.1090" [Broken]

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So, if I empty my bank account, I am flat broke, but if I overdraw by $1, I am the richest person in the universe?http://arxiv.org/abs/0907.1090" [Broken]

Just what does it mean to be "greater than infinity"?

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negitron

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Ask Rom R. Varshamov and Armen G. Bagdasaryan. They wrote the paper, apparently.Just what does it mean to be "greater than infinity"?

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This sounds like the end result one would obtain by applying twos-compliment arithmetic to the set of {reals, infinity}.

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a < b

Hence, how in the world is negative numbers greater than infinity?!

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Hmm. I've never heard this kind of math before. Thanks for sharing with us, very interesting one.

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arildno

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To begin with, the authors seems to confuse concepts like axioms and conditions.

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What matters is if the results derived in the paper are useful. I mean, when Dirac wrote in his book: "principles of quantum mechanics" that the derivative of Log(x) should contain a term proportional to a so-called "delta function" that he had just invented out of thin air a few pages back, was complete nonsense too. The whole notion of a delta function in the way he explained it, was inconsistent in the first place.

To begin with, the authors seems to confuse concepts like axioms and conditions.

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CRGreathouse

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They're giving up transitivity, which is a pretty big blow. What does their system gain?

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They're giving up transitivity, which is a pretty big blow. What does their system gain?

I only had a quick look yesterday. It seems to me that the gain is that you have a more efficient formalism for doing computations involving divergent series.

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Office_Shredder

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I'm stuck on definition 2.1. How is that supposed to work for 0?

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CRGreathouse

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Using footnote 2 and certain bad assumptions you can give it the intended order where 0 is less than any nonzero element. If their caviler attitude bothers you, let 2.1 apply only to nonzero numbers and adjoin 0 in such fashion.I'm stuck on definition 2.1. How is that supposed to work for 0?

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I think it works to their disadvantage to use existing notation like [tex]\sum_{n=a}^b f(n)[/tex] with their new meaning. Better would be using a different notation.

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Hurkyl

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Mentallic

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You've managed to change my ideas on this paper from "majorly screwed up" to "some pretty cool stuff"

Where do the integers switch from positive to negative? In our accustomed number system, zero is basically the turning point, but for this system in my eyes it seems to be 1/0 which suggests there is no switch, but a grey fuzzy area of [tex]+\infty \rightarrow -\infty[/tex] ??a new method for ordering the integers, from which we get Z =

[0, 1, 2, ...,−2,−1]

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arildno

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Sure enough, it just seemed extremely amateurish at first glance not the least the initial discussion concerning the "correctness" of the 18th century view, which they seemed to espouse.What matters is if the results derived in the paper are useful. I mean, when Dirac wrote in his book: "principles of quantum mechanics" that the derivative of Log(x) should contain a term proportional to a so-called "delta function" that he had just invented out of thin air a few pages back, was complete nonsense too. The whole notion of a delta function in the way he explained it, was inconsistent in the first place.

If they had said that they had been INSPIRED by that view to construct a new number system, rather than pushing for its "correctness", I would have been less suspicious of it.

I haven't bothered to look much further into it, I'll admit.

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I think "amateurish" is apt. It seems clear neither author is a mathematician. But (unlike most papers with that characteristic) this seems to have some good content. Maybe what they need is a mathematician (or mathematics student) to take their material and write it in a more acceptable form. Maybe with some other notation... replace the new [tex]\Sigma_a^b \;f(n)[/tex] with [tex]{\mathbb{S}}_a^b \;f(n)[/tex] or [tex]{\oplus}_a^b \;f(n)[/tex] and something similar for the new limitSure enough, it just seemed extremely amateurish at first glance.

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I really don't see anything that is unclear about the usual ordering of the integers.However, some properties of negative numbers had been remaining unclear for a long time, in particular, the order relation between positive and negative numbers.

That is, they used the wrong quotation mark in LaTeX, should be ``nothing''”nothing”

Definition 2.5 is nothing but a telescopic sum.

I stopped reading after that.

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CRGreathouse

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I think inexperience ("amateurish" as arildno and g_edgar) + hubris suffice to explain those.Here are some telltale signs of crackpottery:

The paper seems fine to me. I don't know if it's interesting or not, though.

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That's true, I take it back.

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