## Wrong on the Internet: John Gabriel

For the discussion of math. Duh.

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silverhammermba
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### Wrong on the Internet: John Gabriel

John Gabriel is a self-titled "philosopher/mathematician" with some pretty radical ideas.

First off, he does have some interesting mathematical work. He has thought up some alternate formulas for computing Riemann integrals and performing basic calculus but ultimately it's nothing that amazing. But what makes him so special? John HATES irrational numbers.

He's a pretty frequent writer of Google knols (units of knowledge) and though his knols on calculus are pretty lucid and well-written, if you get him started on irrational numbers he goes off the deep end... fast.

For example, he thinks that the real numbers are countable
Well, not really, because he really thinks that real numbers (irrational numbers) are not "well-defined"

What makes him so lovable:
• His arguments are riddled with contradictions and circular logic (can you spot his assumption that all numbers are rational?)
• His primary reference is himself and he does so in third person. He'll quote himself in his own articles and then put "-John Gabriel" at the end. Or He'll say "...using John Gabriel's integration formula."
• He frequently interrupts his own arguments to start ranting about how everyone else is a blind fool
• He deletes all comments on his knols and disables comments on his blog. Just like anyone interested in academic discussion
• He thinks real analysis is complete bullshit

What sort of disturbs me:
• Almost all of his knols are really well-rated. How?

Basically he doesn't seem to understand how axiomatic mathematics work, he's incredibly close-minded when it comes to alternate definitions of concepts, and he seems to have a fundamental misunderstanding of what limits are. He'll often talk about the limit of a number... which is meaningless.

His knol page: http://knol.google.com/k/john-gabriel/-/nz742dpkhqbi/0#
His blog: http://mathphile.blogspot.com/

Syrin
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### Re: Internet Crazy Person: John Gabriel

I think I had to stop reading that article when he "debunked" the countability of the rationals.

phlip
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### Re: Internet Crazy Person: John Gabriel

Syrin wrote:I think I had to stop reading that article when he "debunked" the countability of the rationals.

Don't worry, later on in the same article he uses the countability of the rationals as part of his reasoning for the countability of the reals.

As far as I can parse it, and translated from crazy into maths, his reasoning is:

There is a bijection from the naturals to the decadic rationals in [0,1) (that is, the numbers with a terminating representation in decimal). This is not, however, a bijection between the naturals and the reals in [0,1), but that's OK, because it's also not a bijection between the naturals and the rationals in [0,1), but the rationals are countable. So obviously, the function not being a bijection isn't a barrier to the set being countable, therefore the reals are countable.

I think this is similar to his original reasoning that the rationals aren't countable up the top... he doesn't get De Morgan's law, and conflates "there doesn't exist a bijection" with "there exists a not-bijection".

Him dealing with the decadic rationals also seems to tie into his "the reals aren't well-defined", or at least, the first few paragraphs of it, since that's all I read... he seems to buy into the common-among-maths-newbies belief that terminating decimals are somehow more "real" than non-terminating decimals, which are less numbers and more "processes" that "tend towards" a number.

Another thing about his "the reals aren't well-defined"... a bit later he starts talking about how irrational numbers apparently exist in reality, but not in theory. I always enjoy people who this angle... I'll never understand the mindset that something could be "true in theory but false in a theoretical reality" when the theory is designed to control that theoretical reality. Last time I saw this was in a Monty Hall thread (I think, could be another similar puzzle), where someone was saying that, in practice, switching will let you win 2/3 of the time, but in theory, the probability is still 50%.

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### Re: Internet Crazy Person: John Gabriel

Flawed logic will lead to flawed conclusions. Apparently he hates theoretical physics, too:

He agrees with this guy that Einstein was an idiot and that special/general relativity are complete bullshit because he doesn't understand them (and thus nobody else does, either. His comment is at the bottom of the page).

Which is funny, since Einstein's theories have kind of been proven to be true, but whatever...
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antonfire
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### Re: Internet Crazy Person: John Gabriel

They have not been "proven to be true", they have been experimentally verified to pretty good accuracy.

Anyway, I wrote a long-ass comment on there, since, amusingly enough, the only complaint he "allowed" people to comment with is the correct response to his argument. (He should have forbidden anyone from posting any response other than

Since it's almost certainly never going to see the light of day, I think I'll post it here too.
Spoiler:
1/3 is a number between 0 and 1 which does not appear in your tree.

If, as you say, 1/3 appears in your tree, and if, as you say, the tree can be put into one-to-one correspondence with the natural numbers, then which natural number does 1/3 correspond to?

At any rate, the mistake in what you wrote as "the proof that the positive rational numbers are countable" is yours, not Cantor's.

Here is the actual proof. Start following the arrows in the diagram and assign natural numbers in order to the rationals you hit, _but_ skip any number you have seen before. That is:

Start at 1/1. This is the rational number corresponding to 1.
Move on to 2/1. We haven't seen this before, so this is the rational number corresponding to 2.
Move on to 1/2. We haven't seen this before, so this is the rational number corresponding to 3.
Move on to 1/3. We haven't seen this before, so this is the rational number corresponding to 4.
Move on to 2/2. We have seen this before (1/1), so we skip it.
Move on to 3/1. We haven't seen this before, so this is the rational number corresponding to 5. (Not 6!)
and so on.

With this, for every positive rational number, there is one and exactly one natural number corresponding to it. For example, the only natural number corresponding to 5/2 is 13. The only natural number corresponding to 22/7 is 248.

And for every natural number, I can find one and only one positive rational number corresponding to it. For example, the only positive rational number corresponding to 11 is 5/1. The only positive rational number corresponding to 1000 is 1/57. The only positive rational number corresponding to 10000 is 60/121.

Give me a positive rational number and I could, after some work, tell you exactly which natural number it corresponds to. Give me a natural number, and I could, after some work, tell you exactly which positive rational number it corresponds to.

This is the sense in which the positive rational numbers are countable: There is a correspondence between them and the natural numbers such that each positive rational number corresponds to exactly one natural number, and each natural number corresponds to exactly one positive rational number.

Now I believe I understand the correspondence you have constructed with the tree: 0.0 corresponds to 1. Then 0.1, 0.2, through 0.9 correspond to 2 through 10. Then 0.01, 0.02, ..., 0.09; 0.11, 0.12, ..., 0.19; ...; 0.91, 0.92, ..., 0.99; correspond to 11 through 100, and so on.

For example, the natural number corresponding to .3 is 4, and the one corresponding to .314 is 383. The number corresponding to the natural number 7 is .6, and the one corresponding to 1024 is 0.0026.

If what you claim is a one-to-one correspondence between [0,1) and the natural numbers, however, then you should be able to find a natural number corresponding to 1/3. What number is it? It is not 1; that corresponds to 0, which is not 1/3. It is not 4; that corresponds to 0.3, which is not 1/3. It is not 400; that corresponds to 0.333, which is not 1/3.

Is there such a natural number? If so, what number is it?

If you don't feel like computing it, can you at least tell me which level of the tree contains 1/3? It is not the first level; that only contains 0. It is not the second level, that only contains .1, ..., .9. Is it the seventh level? The hundredth? The 81278'th?
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

Syrin
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### Re: Internet Crazy Person: John Gabriel

After skimming through some other of his "knols", or whatever they are, I have come to the conclusion that this man is beyond help. His arguments against the well-definedness of irrational numbers were just silly. Something along the lines of "We define it to be the limit of a sequence of rational numbers, but that presupposes that the limit exists!", apparently forgetting that each irrational number is just a mathematical object that we say has this property. I guess, for him, you can't just create arbitrary mathematical constructions out of nowhere.

Which is ironic, given that he seems to be perfectly fine with the complex numbers.

silverhammermba
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### Re: Internet Crazy Person: John Gabriel

antonfire wrote:They have not been "proven to be true", they have been experimentally verified to pretty good accuracy.

Anyway, I wrote a long-ass comment on there, since, amusingly enough, the only complaint he "allowed" people to comment with is the correct response to his argument. (He should have forbidden anyone from posting any response other than

Don't waste your effort. A while back when I first discovered this guy I posted a similar comment in which I also pointed out that in showing that the reals are countable he's assuming that all real numbers are rational (since any number with a terminating decimal expansion is rational), and my comment has yet to see the light of day. This guy has an indomitable "I'm right, you're wrong!" attitude.

Yakk
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### Re: Internet Crazy Person: John Gabriel

How is this particular person that interesting? I mean, he's wrong: but being wrong on the Internet isn't that interesting.

He is stubborn, apparently. So what can this thread produce, other than (say) him self-googling and finding this thread? (remember, xkcd has a ridiculous pagerank).
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

Blatm
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### Re: Internet Crazy Person: John Gabriel

Wrong on the internet can be interesting. Timecube certainly was, and so was that INVERSE ZERO guy from a while back (whose post I didn't save anywhere unfortunately). I can imagine this guy being interesting too in the same way, though I haven't read through his stuff yet.

john_gabriel
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### Re: Internet Crazy Person: John Gabriel

So you think I am a self-titled philosopher/mathematician? This is funny. I did not know anyone had to have your approval or anyone else's to be a philosopher or mathematician.

You have quite a bizarre view of my work. Let me say that you are way off the mark. You might be better off if you actually understood what my work is all about.

Your comment on this forum demonstrates you do not understand my work.

I do not hate irrational numbers or anything else. Were you smoking something quite strong before you read my knols? This again is pathetic. Please tell me what is so hard for you to understand and I might attempt to explain it further.

I suggest you reread these articles several times - your answers lie therein:

Link removed for breaking forum rules. - gmalivuk

You have reached several incorrect conclusions.

You write: "Almost all of his knols are really well-rated. How? "

Well, my friend, one is always disturbed by what one does not understand. The knols are highly rated because the content of these knols make sense - something that can't be about what you write or say.

I may or may not respond to you. What do I owe you? Nothing. Either way, you have no right to call me an internet crazy person. I suggest you remove this post or apologize for it.

jestingrabbit
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### Re: Internet Crazy Person: John Gabriel

First up, your second sentence is wrong. A set is countable if there is a bijection between it and the natural numbers. A set is infinite if there is a bijection between it and a subset of itself, or alternatively if there is an injection from that set to itself which is not a bijection.

Frankly, if you're going to go around spouting stuff that is false, getting basic definitions wrong, and then ignoring people who make a reasonable attempt to correct your errors, I do think that you've let your readers down. You owe people corrections.
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Yakk
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### Re: Internet Crazy Person: John Gabriel

Yakk wrote:How is this particular person that interesting? I mean, he's wrong: but being wrong on the Internet isn't that interesting.

He is stubborn, apparently. So what can this thread produce, other than (say) him self-googling and finding this thread? (remember, xkcd has a ridiculous pagerank).

I rest my case.

John Gabriel has (apparently) registered for these forums, having seen this thread as the 8th hit for John Gabriel mathematics (or math, apparently). John Gabriel's thread on xkcd being that highly ranked is funny. . . I'm guessing by googling Mathematics (or Math) and John Gabriel, or using that google thing where you get reports of new websites talking about a certain subject? What is that tool called again...
Last edited by Yakk on Thu Dec 03, 2009 2:55 pm UTC, edited 1 time in total.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

Xanthir
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### Re: Internet Crazy Person: John Gabriel

This does do quite a bit to show why the Knol system is fundamentally flawed. Anyone can create and lock down a knol, preventing further corrections to it. Thus wildly incorrect things get the stamp of approval from being a knol, and receive the pagerank from being in the system. J. Random Crackpot usually just posts their blatherings on badly-maintained geocities-era websites that no one looks at (and who receive pagerank only ironically).
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antonfire
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### Re: Internet Crazy Person: John Gabriel

john_gabriel wrote:I suggest you reread these articles several times - your answers lie therein:

John, we are here because we have read this, and are pointing out that it contains several misunderstandings and several outright mistakes.

If you want to discuss the objections people have made to what you've written, I suggest you open up the comments on your own site. Barring that, I suggest you at least address the issues that people have brought up, rather than the tone with which they've brought them.

And no, you have not addressed them with your chain of edits to the original post. And until you do, you certainly shouldn't be wasting your time complaining that people have called attention to it. When people consistently tell you that you are mistaken, the appropriate response is to seriously consider the possibility that you are, not to get angry at the world.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

john_gabriel
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### Re: Internet Crazy Person: John Gabriel

antonfire wrote:
john_gabriel wrote:I suggest you reread these articles several times - your answers lie therein:

John, we are here because we have read this, and are pointing out that it contains several misunderstandings and several outright mistakes.

If you want to discuss the objections people have made to what you've written, I suggest you open up the comments on your own site. Barring that, I suggest you at least address the issues that people have brought up, rather than the tone with which they've brought them.

And no, you have not addressed them with your chain of edits to the original post. And until you do, you certainly shouldn't be wasting your time complaining that people have called attention to it. When people consistently tell you that you are mistaken, the appropriate response is to seriously consider the possibility that you are, not to get angry at the world.

Perhaps the problem lies more with your brain than my knols?

antonfire
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### Re: Internet Crazy Person: John Gabriel

Unlikely: I have pointed out a few mistakes in what you have said. You have made no statements with any mathematical content.
Last edited by antonfire on Sat Nov 28, 2009 3:34 pm UTC, edited 1 time in total.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

john_gabriel
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### Re: Internet Crazy Person: John Gabriel

Xanthir wrote:This does do quite a bit to show why the Knol system is fundamentally flawed. Anyone can create and lock down a knol, preventing further corrections to it. Thus wildly incorrect things get the stamp of approval from being a knol, and receive the pagerank from being in the system. J. Random Crackpot usually just posts their blatherings on badly-maintained geocities-era websites that no one looks at (and who receive pagerank only ironically).

I don't think so. You are the reason I am glad the Knol system prevents any editing - I would not allow anyone of inferior intelligence to edit my work. Sorry, but there is simply no way I shall open up my knols to comments, especially when there are those like you who have nothing better to do than post flaming comments.

If anyone on this site is so sincere, how is it no one has responded to my offer? I said I might be prepared to help you understand by debating the topic with you on your forum. To be quite frank with you, I don't know if I shall even bother visiting your site again. What don't you understand? Tell me and I might address it - here on your site. I don't want garbage appearing all over my Knols.

antonfire
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### Re: Internet Crazy Person: John Gabriel

john_gabriel wrote:If anyone on this site is so sincere, how is it no one has responded to my offer? I said I might be prepared to help you understand by debating the topic with you on your forum. To be quite frank with you, I don't know if I shall even bother visiting your site again. What don't you understand? Tell me and I might address it - here on your site. I don't want garbage appearing all over my Knols.

Sincerity would be discussing it on your own page where everyone who sees it will see the discussion. Still, I suppose we take what we can get.

I don't understand which level of your tree, if any, contains the number 1/3.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

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### Re: Internet Crazy Person: John Gabriel

Also, please respond to jestingrabbit's post:
jestingrabbit wrote:First up, your second sentence is wrong. A set is countable if there is a bijection between it and the natural numbers.
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Yakk
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### Re: Internet Crazy Person: John Gabriel

Very well.

Some may argue since it is not possible to write decimal numbers that are infinitely represented, the same cannot be included in the above tree. Such an argument is untrue because the rational numbers which are countable, contain members not represented finitely in every radix system.

This paragraph in particular is wrong. You claim to have proven that you can count every real number form [0,1] by counting only the numbers that can be finitely represented. Then you admit there are non-finitely represented real numbers. So your prior proof doesn't prove what you claim it did.

In order to prove that the real numbers from [0,1] are countable, you have to count them (create, at the very least, a surjection from the natural numbers to the real numbers from [0,1]). If you count some subset of the real numbers on [0,1], you have not proven they are countable.

I agree that the set of finitely long decimals in [0,1] are countable. This does not imply that the set of real numbers on [0,1] are countable.

---

Back to Cantor.

Cantor's proof may rely on the fact that you can represent every real number in [0,1] by a possibly infinitely long decimal: however, Cantor could merely prove that the subset of real numbers that can be represented as decimals (possibly infinitely long) are uncountable, then that a set A containing a set B is as least as large as the set B.

So, let X be the set of real numbers from [0,1] such that they can be represented by a decimal (possibly infinitely long decimal).

X is clearly a subset of the reals, so the reals are going to be larger.

Now, if there is a bijection bewteen the natural numbers (0,1,2,.. etc) and the reals, there will be a surjection from the natural numbers to a smaller set (like X).

Let F: N -> X (F is some function, it maps natural numbers to the set X) be a sujrection from the naturals to the reals. I'm going to prove (via Cantor's method) that F cannot exist. If F cannot exist, then there is no bijection between the natural numbers and the reals. Make sense so far?

So for any real numbers that can be represented as decimals in [0,1], for example "r", if F exists, there is a natural number k such that F(k) = r. And we must be able to do this for each element of X.

Let D(n, r) extract the nth decimal digit of the real number r.

Then we define our real number q as follows:
D( i, q ) = 5 if D( i, f(i) ) != 5
D( i, q ) = 1 if D( i, f(i) ) = 5
with whole part 0.

Now, q can be represented as a decimal number, and it's value is in [0,1]. So q is in our set X.

By the assumption of the properties of F, there is some natural number (call it m) such that f(m) = q.

What is the value of D( m, q )? Clearly it is 5 or 1, given how we defined q.

If D(m,q) is 5, then D(m, f(m)) != 5, from how we constructed q. This cannot happen if f(m) = q.

If D(m,q) is 1, then D(m, f(m)) = 5 from how we constructed q. This clearly cannot happen if f(m) = q.

Both possibilities are looked at, and thus we have reached a contradiction. The assumption we made was that F was as surjective function from N to X -- so we have proven no such function exists.

As there is no surjection from the natural numbers to our set X (which is a subset of the Reals), there cannot be a bijection from the natural numbers to the Reals, so the cardinality of the Reals is greater than the Natural Numbers.

First question: Anyone besides JG find an error in my logic?
Second question: At what step you you object to my logic, JG? I understand you object to my conclusion: I'm asking for what step caused you problems.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

Captain_Thunder
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### Re: Internet Crazy Person: John Gabriel

You should also respond to Syrin's most recent post regarding the definition of irrational numbers as limits of sequences of rational numbers, JG; such a definition isn't contradictory at all. In fact, we do that all the time in math, where we start off by defining an object as having one particular property and then trying to derive its other properties, without any regards as to whether this object "already exists" or not.

EDIT: Reading over his "Are the real numbers well-defined?" post, he seems to be some sort of ultra-hardcore constructivist with a disdain of anything "abstract". Aside from the actual technical errors, there's nothing inherently wrong with adopting that philosophy, although it doesn't make you any more right than people with different philosophies.

Yakk
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### Re: Internet Crazy Person: John Gabriel

Defining irrational numbers as limits of rational numbers is a bit sloppy. Which, fortunetally, isn't how we define irrational numbers usually.

Instead, we define what it means to be a Cauchy sequences of rational numbers. These 'exist', and aren't hard to find. Then we call them the real numbers once we bundle them into equivalence classes (two Cauchy sequences, when pair-wise subtracted, end up getting arbitrarily small, are deemed equivalent), and look at their properties.

These properties are very number-like (they can be added, subtracted, multiplied, divided (except 0), exponentiated, all without much definition work, in ways that are 'number-like' (they are a field)). And we can embed the rational numbers in them in a pretty easy fashion. As a bonus, we get neat results like "all closed and bounded sets have a greatest element", which make other kinds of math much much easier. You could try doing calculus on the rational numbers, but I think it would be a headache (for an example of what type of headache, look at constructive analysis by Bishop and Bridges, where they do analysis on the constructive reals -- then compare the results to a standard analysis text).

We can even build a surjective map from the set of possibly infinitely long base 10 decimals to these real numbers (surjective, because we do end up with 0.9999... and 1.0000... both mapping to the same equivalence class) that behaves nicely in that the conventional map from finitely long decimals injectively to the rational numbers maps to the same values we embed the rational numbers as in the reals.

But at this point, I'm using a bunch of terminology in very technical senses: it is next to technobabble. Odds are I even made a mistake in my previous paragraphs: so someone who doesn't already know what I'm babbling about would find the above to be both nonsense, and probably be led astray by my own screwup or typo. So this post isn't very useful, other than at best as a high-level roadmap on what mathematicians are talking about when they talk about the "real numbers".
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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### Re: Internet Crazy Person: John Gabriel

john_gabriel wrote:To be quite frank with you, I don't know if I shall even bother visiting your site again. What don't you understand? Tell me and I might address it - here on your site.

If you do come back to address the numerous objections (and they are objections, not misunderstandings; you're the one misunderstanding, and they're explaining why), you will attempt to be at least moderately civil.
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### Re: Internet Crazy Person: John Gabriel

Laughing my rear end off. This forum is soooo funny.

antonfire
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### Re: Internet Crazy Person: John Gabriel

What level of your tree contains 1/3?
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

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### Re: Internet Crazy Person: John Gabriel

john_gabriel wrote:Laughing my rear end off. This forum is soooo funny.

Indeed. I didn't read this thread long enough to realize that you actually showed up - now that you did, I'm laughing pretty hard too.

But on a more serious note, what do you make of this discrepancy, already noted by jestingrabbit:
John Gabriel wrote:By Cantor's definition, a set is countable if a bijection exists from a subset to itself.

Kolmogorov and Fomin, Introductory Real Analysis wrote:The simplest infinite set is the set Z+ of all positive integers. An infinite set is called countable if its elements can be put in one-to-one correspondence with those of Z+.
This is the definition of countable used in every math book ever written.
Last edited by skeptical scientist on Sat Nov 28, 2009 10:52 pm UTC, edited 1 time in total.
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### Re: Internet Crazy Person: John Gabriel

antonfire wrote:What level of your tree contains 1/3?

Clearly the [imath]\omega^{th}[/imath] level. (Since the surreals are constructed similarly, only with the dyadic rationals at every finite step rather than the decadic, I assume that you'd construct all the finite non-decadic rationals at the same time.)
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### Re: Internet Crazy Person: John Gabriel

skeptical scientist wrote:
john_gabriel wrote:Laughing my rear end off. This forum is soooo funny.

Indeed. I didn't read this thread long enough to realize that you actually showed up - now that you did, I'm laughing pretty hard too.

Google Johen Gabriel Mathematician. And xkcd shows up on the first page. XKCD has ridiculous pagerank.

On top of that, if you have a google alert on that kind of term, we'd show up pretty quickly. Presuming you are a relatively egotistic individual, you are going to google your name/google alert your name/etc.
But on a more serious note, what do you make of this discrepancy, already noted by jestingrabbit:
John Gabriel wrote:By Cantor's definition, a set is countable if a bijection exists from a subset to itself.

Kolmogorov and Fomin, Introductory Real Analysis wrote:The simplest infinite set is the set Z+ of all positive integers. An infinite set is called countable if its elements can be put in one-to-one correspondence with those of √.
This is the definition of countable used in every math book ever written.

To be fair, sometimes it is a one-to-one correspondence with N instead of Z.

The difference is, I'll admit, not even academic.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

RabidAltruism
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### Re: Internet Crazy Person: John Gabriel

Wow, you really called that J. Gabriel would find this XKCD thread, Yakk.

Further proof that neural nets can predict human behavior!
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stephentyrone
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### Re: Internet Crazy Person: John Gabriel

Yakk isn't a neural net, he's a p-zombie.

Next!
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RabidAltruism
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### Re: Internet Crazy Person: John Gabriel

Ah, but there's no mutual exclusivity! He could very well be a p-zombie driven by a neural net.
...she reminds you of the invisible form of the soul; she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth...

skeptical scientist
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### Re: Internet Crazy Person: John Gabriel

Yakk wrote:XKCD has ridiculous pagerank.

I've noticed that.

Yakk wrote:
Kolmogorov and Fomin, Introductory Real Analysis wrote:The simplest infinite set is the set Z+ of all positive integers. An infinite set is called countable if its elements can be put in one-to-one correspondence with those of √.
This is the definition of countable used in every math book ever written.

To be fair, sometimes it is a one-to-one correspondence with N instead of Z.

It is a one-to-one correspondence with N; they're just calling it Z+ instead. Although I see I had a typo.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

RabidAltruism
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### Re: Internet Crazy Person: John Gabriel

skeptical scientist wrote:
Yakk wrote:XKCD has ridiculous pagerank.
It is a one-to-one correspondence with N; they're just calling it Z+ instead. Although I see I had a typo.

Z+ just means "all integers which are positive" -- i.e., the natural numbers, or N, right? I thought that was pretty broadly accepted notation.
...she reminds you of the invisible form of the soul; she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth...

Yakk
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### Re: Internet Crazy Person: John Gabriel

Ooops, that is what I get for skimming. I missed the little +, and the word positive.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

Syrin
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### Re: Internet Crazy Person: John Gabriel

The problem with discussions on Internet Crazies is that some people will make disparaging remarks (you know, due to the crazy), so any legitimate arguments might be overlooked when said Crazy decides to join in on the fun.

As is made evident by this very thread.

I can imagine him looking at the thread, reading all the replies, and then walking away from his computer, shaking his head while quietly mumbling to himself - "their feeble minds cannot even begin to *unintelligble* GENIUS I tell *unintelligble* why won't they just realize that I *unintelligble* DEATH TO THE IRRATIONALS, ALLAHU *unintelligble*"

Edit: also, I know when I said "we define the reals as the limits of rational numbers" (paraphrased), that I was, technically speaking, not correct - the entire time I was writing it I was wondering to myself whether or not somebody would call me out on it. I guess I should know better than to take a small liberty on a mathematics forum. :\

skeptical scientist
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### Re: Internet Crazy Person: John Gabriel

Syrin wrote:Edit: also, I know when I said "we define the reals as the limits of rational numbers" (paraphrased), that I was, technically speaking, not correct - the entire time I was writing it I was wondering to myself whether or not somebody would call me out on it. I guess I should know better than to take a small liberty on a mathematics forum. :\

Meh, I didn't have a problem with it. It's exactly the motivation behind the Cauchy sequence definition, and it is what we are doing in spirit. Explaining the motivation is often much easier to understand than explaining the abstract details, even if it is less precise.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

RogerMurdock
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### Re: Internet Crazy Person: John Gabriel

Oh my god, I'm laughing so hard right now. The timing...it's just perfect. I scrolled down, read Yakk's comment, then immediately my eyes jumped down to this guys post. PRICELESS.

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### Re: Internet Crazy Person: John Gabriel

silverhammermba wrote:a self-titled "philosopher/mathematician" with some pretty radical ideas.

Bzzzzt! I got it!

"What is a crank?"

Next, I'll take logical fallacies for 400, please.

Professors of mathematics who teach the subject of real analysis will tell you on the one hand that all real numbers can be represented using the decimal number system, and on the other hand that the real numbers are uncountable. This is a contradiction, for if the real numbers are uncountable, then not all numbers can be represented using the decimal number system.

Can you spot the place where he forgot the significance of the term "non-infinite"?
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### Re: Internet Crazy Person: John Gabriel

Yakk wrote:
skeptical scientist wrote:
john_gabriel wrote:Laughing my rear end off. This forum is soooo funny.

Indeed. I didn't read this thread long enough to realize that you actually showed up - now that you did, I'm laughing pretty hard too.

Google Johen Gabriel Mathematician. And xkcd shows up on the first page. XKCD has ridiculous pagerank.

Justified though, as we can clearly see from this thread.

Imagine an undergrad math student stumbling upon some of this guy's work. He thinks it's interesting and wants to know more about it. So he googles this guy. Finding this thread on top will save him a lot of hours of reading bullshit, as well as potential embarresment in front of his teachers.
It's one of those irregular verbs, isn't it? I have an independent mind, you are an eccentric, he is round the twist
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Lord Aurora
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### Re: Internet Crazy Person: John Gabriel

xkcd: saving math majors from embarrassment since the mid-2000s.
Decker wrote:Children! Children! There's no need to fight. You're ALL stupid.