753:: It seems like something someone would have thought about before, and maybe there is another source out there. But this is just speculation. All we got so far is that Schroeppel made up this term "radical integer" in a discussion on a mailing list, with the help of others he proved some results in the list discussion, Weisstein mentions this in his encyclopedia. That's not enough. Now, I've often thought Knowledge is too stringent at times, but what about in this case? I feel it's wise. I mean, who are we supposed to credit the theorem? Schroeppel says it wasn't just him. What about the proof of the stated result? Are we just supposed to state the result and then not say anything more? If Schroeppel put it up on his webpage, it would be different (for me and some others I'm sure), but he says he can't find the preprint! It seems that maybe he could find it, but he says that it assumes too much knowledge of the list discussion, so it's possible editors trying to use the preprint to create the article would have to violate
672:. I know we don't like mailing lists, but math mailing lists that reputable researchers use show that the idea has some exposure in its area. Furthermore, per kotepho, the fact that this is contained in a book makes it verifiable, regardless of the original source OF the book; when a book is published we can trust that the author and publisher vet their sources, and if it's good enough for them, it should be good enough for us, as long as there's no reason to suspect bias. Frankly, I'm surprised this concept originated as late as 1997! Schroeppel (below) doesn't mention any source he got it from, but that doesn't mean one doesn't exist.
403:. There just does not seem to be enough to establish this as even a somewhat marginally used number theoretic term. We definitely should not create Knowledge articles based on basically one Internet posting by even a respected researcher; it's not even clear whether he is using it as standard terminology or it's just a temporary term he made up. Just because Weisstein and MathWorld have chosen to propogate this terminology does not make this standard terminology. --
738:. He apparently got this idea somehow (from looking at outdated books, I imagine) and then goes on a whole long spiel about how topologists and geometers differ on what to call the 2-sphere. In my experience also, his error ratio is quite high, and his goofs can be quite bad. What's funny is that he goofed on the entry under discussion, but I suppose that's not really going to change your mind as to reliability. --
734:
as
Knowledge's. Not only that, but no, we don't just trust the author and publisher. In particularly contentious cases (as in this one), what is usually done is that we look into whether the author is reliable. This reminds me of the time Weisstein claimed (and still does) that geometers don't use 2-sphere to refer to a
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report what they said as fact. In the rare case that their mere reporting of the alleged facts is notable, as opposed to the facts themselves, then certainly we can say that's what they said. That's clearly not the case here; the fact that MathWorld uses a term is not in itself worthy of encyclopedic
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I was refering to Schröppel as credible, not
Weisstein. Even given that I think that the book has inaccuracies that does not proclude us from reporting what it reports and not asserting anything (which is what we should be doing). The New York Times screws up and we still use them as a source, no?
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I'm not all that persuaded that it's obvious a "radical integer" should be a "radical number" that's at the same time an algebraic integer, and anyway I don't recall hearing "radical number" before (may be internal terminology to Maple). Unless the term can be better attested, I don't think WP should
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under these circumstances, rather than simply inferred by the reader by looking at the references, given that the proof hasn't had formal peer review. I might feel differently if we had the proof available to us to check; "legalistically" I suppose that's not supposed to make any difference, but I'd
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so the relevance would be to the claimed result (namely that if a number expressible by radicals starting with rationals is an algebraic integer, then it can be expressed by radicals starting with ordinary integers). As I say, that's a nice result, but I don't think that from the sources we have, we
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Verifiability doesn't mean we don't make distinctions among sources. We don't have to blindly accept everything that gets an ISBN. We don't really know what Schröppel said, and anyway he doesn't seem to be a number theorist either. For that matter even if he were a number theorist, his use of a term
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per
Trovatore. If some evidence could be provided that the term is more widespread than is suggested by what's been written so far during this discussion, then I might be persuaded to change my mind. Certainly if Weisstein and an offhand definition in a mailing list discussion are the only sources,
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source (it's unfortunate that
Schroeppel's email, posting, etc., can't be used, but that's how it is); this one source is an encyclopedia, a source whose authority and reliability is supposed to rest on the sources it cites. In this case, it's clear that this source's standard are not as stringent
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After searching the web for a little while, it seems that this R Schroeppel character is a bona fide researcher in the area of theoretical cryptography. You can find lots of published papers by him on some fairly mathematical topics. But I found no reference for radical integers. It seems like a
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The only given reference is to
Weisstein at MathWorld; his only reference, in turn, is to a "math-fun@cs.arizona.edu posting, May 11, 1997", whatever that means, by one R. Schroeppel. The definition itself seems like a reasonable one to make, but people who want to make up words should publish them
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I don't think you can say that what this article and MathWorld are saying is untrue, just that is isn't notable. I am not sure that it is notable, but my bar is low because we are not made of paper. However, the searching I have done has not found anything else either so it is unlikely that this
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the golden ratio a "radical integer"? You'd think this result (the general one, not just for the case of the golden ratio) might be the sort of thing RS might have gotten around to publishing if the proof had held up, which makes me wonder if he found a mistake later. This has gotten mildly more
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and I can find other mentions of "radical number" on the web. So a "radical integer" by the definition in this page is exactly what one would expect it to be, namely a radical number that's also an algebraic integer. But it doesn't seem to be used enough to merit its own article.
421:, which the Internet posting clearly does not. In terms of verifiability, MathWorld may not work either, as Arthur (below) has casted doubt on the article's validity; given there is at least one mistake there, we really need access to the original posting. --
81:: I looked for it on Google and it is mentioned on a few educational sites, especially in China, but none of them work. Some of the stuff on Weisstein's is crap, at least the science encyclopedia, but I don't know enough math to make a decision on this. --
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page. Could be he knows something more specific about it. But if that traces back to
Weisstein too, I think we have to delete. Verifiability is not a suicide pact, and we don't have to jump off every cliff Eric jumps off.
382:, do not merge. There is just not enough source material to make a solid article about this: we have Weisstein's encyclopaedia, citing an email, and the Maple help file, which uses another term. I found one reference to
97:. As the article notes, the "radical integers" are a subring of the algebraic integers, and the algebraic integer article already mentions them in passing. Anyway, I'm not sure this is quite a neologism: for example,
687:
The more I think about this, I think the notability of this term is negligible, and so we should merge it rather than keeping it as an article on its own. I still believe it's adequately verifiable, however.
712:
rely on
Weisstein!!! Talented as he obviously is, his quality control standards just aren't good enough in this sort of area. What's good enough for Weisstein should not be automatically good enough for us.)
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serious; the issue now is not just whether MathWorld is pushing a non-accepted terminology, but whether they've made an actual mathematical error here. But it's definitely an interesting result if true. --
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have enough to claim in WP that it's true. If we could verify the result, then there might still be a question whether "radical integer" is genuinely accepted nomenclature for the concept. But if we
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I have no problem reporting what he is reporting from a decently credible source. I'd love to see the mailing list post or other papers, but I think this meets our standards without them.
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Schroeppel claims to have proved it himself. He probably did, and it's a nice result that would be nice to have. Unfortunately it hasn't been published in a reliable source. (People, we
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not sure if its a radical integer. Radical numbers are not the same as algebraic integers, 22/7 is a radical number but not an algebraic integer. I've emailed
Schroeppel. --
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does not say that we just include anything that we can verify, it's necessary that the sources be reliable also. Here we have an article whose contents are backed up by
800:. Don't see the relevance of the concept. One could as well define "square root radical integers" where taking roots is restricted to square roots. Relevance matters.
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Sorry, I don't buy it. If
Weisstein were a number theorist it might be different, but he's not. His choice of terminology should count for approximately nothing. --
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very noncontroversial definition, but I suppose we can't allow even noncontroversial definitions that are in violation of NOR, right? If this is a violation of
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a "decently credible source", on this topic. He has kind of a history of putting dubious and poorly-attested mathematical terminology in his enclyclopedia. --
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I am not sure about that; Schroeppel clearly claims to have proved it, and if we source it to him, we are doing our job (and it's the sort of thing which
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Not a bad idea. Not me, though, I think. Anyone who wants to can find the e-mail in the history; I think we shouldn't leave it here on the page. --
112:, or a combination of roots of rational numbers specified in terms of radicals. A sum, product, or quotient of these is also a radical number.
155:, merging is not appropriate, we have to delete. If it turns out not to be a violation, then let it stay in its own article. -
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in one posting on a mailing list wouldn't constitute much evidence that it's an accepted term in the number theory community.
477:? The mathworld article claims such, but it also claims there are cubic equations which are not solvable by radicals. —
98:
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I doubt it's encyclopedic if stated as "Schroeppel claims to have proved...", which would clearly have to be in the
237:. We want to be verifiable and don't really care about truth. My qualms about MathWorld's accuracy do not matter.
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wow, good catch, I hadn't noticed that at all. Maybe the article meant "quintic"? Anyway now I'm sort of curious;
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Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a
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Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a
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verify the result, then as you say, keeping the term (even as a redirect, I think) would be kind of silly. --
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for me even if we don't get the original source. Is it notable? Dunno, but whats the harm in keeping it?
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on MathSciNet, which was a
Russian paper in the 60s talking about something completely different. --
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853:; if the result has a proof that we can follow, and we check that it's right, then it's verified. --
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concept is worthwhile (at the moment) or that someone would come here looking for an explaination.
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note that the book cited above is by Weisstein, and is therefore not independent confirmation. --
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The content of the radical is 1 + 2φ; that this is φ follows from the Fibonacci relationship.
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The following discussion is an archived debate of the proposed deletion of the article below.
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Excuse me it I restate some of the above. First off we need to distinguish between
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fame. That is not to say he meant "radical integer" to be more than a nonce term.
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article should be rewritten to state the fact without using the terminology. --
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Oh, and by the way, if the New York Times screws up and we find out about it, we
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1 and 3 are both well known, with solid references. Golden ratio is an
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Apparently this is all my fault - sorry. I don't remember the edit
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claim that this is what "radical integer" means, even inside the
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The above discussion is preserved as an archive of the debate.
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A radical number is defined as either a rational number or
101:'s help system defines a "radical number" as the following:
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319:'s talk page; he was the one who added the link on the
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I know it isn't, but it is published. Thus, it is not
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39:). No further edits should be made to this page.
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771:I have a response to this; see the talk page.
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541:{\displaystyle {\sqrt{2+{\sqrt {5}}}}}
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68:in journals like the rest of us. --
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315:However I have left a message on
588:Why don't we just email him at
461:. It may not be the same as a
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725:I agree here with Trovatore.
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441:. I don't really care, but if
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168:. This is Rich Schroeppel of
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507:For the golden ratio, try
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849:call this an instance of
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.