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New evidence that Cantor plagiarized Dedekind?

quantamagazine.org

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Re: New evidence that Cantor plagiarized Dedekind?

#81

Post by ferfumarma »

ozb wrote: post #80

eh this "plagiarism" framing is overreaching there were two proofs in the paper: countability of algebraic numbers and uncountability of reals countability of algebraic numbers is a rather trivial induction on countability of rationals/pairs of numbers, which Cantor already knew about Cantor himself did prove uncountability of real numbers; Dedekind just helped him clean the proof up to me it seems like Dedekind's as…

What a strange interpretation.

As you mention: Dedekind stopped corresponding with him after the publication, but also began keeping a copy of every letter he sent to Cantor.

Sure it's circumstantial, but it's exactly what you would do when you're the victim of a plagiarist.

In my eyes the burden of proof has been met.

Re: New evidence that Cantor plagiarized Dedekind?

#82

Post by globular-toast »

ozb wrote: post #80

eh this "plagiarism" framing is overreaching there were two proofs in the paper: countability of algebraic numbers and uncountability of reals countability of algebraic numbers is a rather trivial induction on countability of rationals/pairs of numbers, which Cantor already knew about Cantor himself did prove uncountability of real numbers; Dedekind just helped him clean the proof up to me it seems like Dedekind's as…

What is this? You used a semicolon (albeit incorrectly) but struggle with full stops? Why are you writing like this?

Re: New evidence that Cantor plagiarized Dedekind?

#83

Post by leethargo »

globular-toast wrote: post #82
ozb wrote: post #80

eh this "plagiarism" framing is overreaching there were two proofs in the paper: countability of algebraic numbers and uncountability of reals countability of algebraic numbers is a rather trivial induction on countability of rationals/pairs of numbers, which Cantor already knew about Cantor himself did prove uncountability of real numbers; Dedekind just helped him clean the proof up to me it seems like Dedekind's as…

What is this? You used a semicolon (albeit incorrectly) but struggle with full stops? Why are you writing like this?

This is to signal non-AI slop?

Re: New evidence that Cantor plagiarized Dedekind?

#84

Post by nobodyandproud »

QuesnayJr wrote: post #25

From the article it's hard to tell if Cantor really did plagiarize (though it seems Dedekind thought he did). According to the article, Cantor proved the theorem first and sent it to Dedekind. Dedekind suggested a simplification of the proof, which Cantor used when he wrote it up. The story doesn't make Cantor look good, but if the original proof by Cantor is correct, then the credit for the theorem still basically b…

The first omission was in my mind forgivable. The second, not so much.

Re: New evidence that Cantor plagiarized Dedekind?

#85

Post by freehorse »

lupire wrote: post #38
zeroonetwothree wrote: post #15

Earlier quoted context omitted.

Complete just means the limit of every sequence is part of the set. So there’s no way to “escape” merely by going to infinity. Rational numbers do not have this property. How to construct the real numbers as a set with that property (and the other usual properties) formally and rigorously took quite a long time to figure out.

Critically, "Complete" also means that the supposed limit necessarily exists .

... for "Cauchy sequences", which are basically sequences whose terms become "closer and closer together".

You can still have sequences with no limits (a_n:=n, going to infinity, where all successive terns differ by 1 and which does not have a limit in the usual metric), as well as sequences with multiple limit points (in which case, subsequences can be considered).

Btw this is "Cauchy completeness", so it is a bit different (but equivalent) way to approach the construction of the real numbers from Dedekind's, but it is also one that can apply to more general metric spaces.

Re: New evidence that Cantor plagiarized Dedekind?

#86

Post by effed3 »

Giving no credits on a "co-author" is a bit different than plagiarize (a theft). It's reasonable to suppose than both authors can have reach results indipendently, given enough time, working on the same matter, maybe Dedekind before Cantor? Probably Cantor has the core ideas in it's mind, and Deedekind's arguments was similar enough to push him proced. Sure Dedeking has given a (big) contribution, but the core concept is from Cantor

Re: New evidence that Cantor plagiarized Dedekind?

#87

Post by effed3 »

sandslides wrote: post #34
dkarl wrote: post #4

> In their 1872 papers, though, Cantor and Dedekind had found a way to construct a number line that was complete. No matter how much you zoomed in on any given stretch of it, it remained an unbroken expanse of infinitely many real numbers, continuously linked. > Suddenly, the monstrosity of infinity, long feared by mathematicians, could no longer be relegated to some unreachable part of the number line. It hid within…

could I just leave my favourite thing ever here? thanks :) https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Gra...

and do not forget this: https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox way more technical, but wonderfull

Re: New evidence that Cantor plagiarized Dedekind?

#88

Post by effed3 »

>> Suddenly, the monstrosity of infinity, long feared by mathematicians, could no longer be relegated to some unreachable part of the number line. It hid within its every crevice.

Exageration, the quite mayority of mathematician live very well with infinity, just handle with care.

Re: New evidence that Cantor plagiarized Dedekind?

#89

Post by ozb »

globular-toast wrote: post #82
ozb wrote: post #80

eh this "plagiarism" framing is overreaching there were two proofs in the paper: countability of algebraic numbers and uncountability of reals countability of algebraic numbers is a rather trivial induction on countability of rationals/pairs of numbers, which Cantor already knew about Cantor himself did prove uncountability of real numbers; Dedekind just helped him clean the proof up to me it seems like Dedekind's as…

What is this? You used a semicolon (albeit incorrectly) but struggle with full stops? Why are you writing like this?

Ah, sorry. I have a (bad?) habit of using newlines as sentence separator in informal contexts, and HN likes to eat newlines if they're not doubled. I'd edit but it's too late now.

Re: New evidence that Cantor plagiarized Dedekind?

#90

Post by tchalla »

jacquesm wrote: post #63
tchalla wrote: post #8

Earlier quoted context omitted.

> since most HN readers should know who Cantor and Dedekind are. Show up with your hands here if you didn’t know either Cantor or Dedekind.

Then you can just skip this submission and nobody will be the wiser.

There are people who like to read about submissions even if they don’t know who the people involved are.
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