Questions tagged [cantor]

Georg Ferdinand Ludwig Philipp Cantor (1845-1918) was a German mathematician who created set theory.

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Equicardinality of $\mathbb{R}$ and $\mathbb{R}^2$ via interleaving decimal expansions

As Fernando Q. Gouvêa notes in his paper, Was Cantor Surprised? (Amer. Math. Monthly 118 (March 2011), 198–209) Cantor initially tried to prove that $(0,1]$ and $(0,1] \times (0,1]$ have the same ...
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Cantor, set theory and foundations

Did Georg Cantor ever think that set theory could serve as a foundational system for all of mathematics? He died in 1918, but Zermelo set theory (just Z, no ZF or ZFC yet) was described in a paper by ...
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When and why Cantor-Hume principle was universally adopted in set theory instead of Euclid's principle?

In this answer and the comments Joel David Hamkins talks about a conflict between Cantor-Hume principle and Euclid's principle. He writes: This principle [Cantor-Hume] is often defended as a ...
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Cantor's later life

I saw this on Wikipedia: In June 1917, he entered a sanatorium for the last time and continually wrote to his wife asking to be allowed to go home. Georg Cantor had a fatal heart attack on January 6, ...
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Cantor's Art of proposing a question

There is a rather famous quotation of Cantor: In mathematics the art of proposing a question must be held of higher value than solving it. It was in a thesis he defended for his doctoral examination ...
Jochen Wengenroth's user avatar
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When did the word "Real number" begin to be used as an official terminology to refer to both rational and irrational numbers?

I am really curious about and struggling with finding when the word "Real number" began to be used as an official terminology to refer to both rational and irrational numbers. In Wiki, it ...
withgrace1040's user avatar
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How was Fourier analysis important to the development of set theory?

I recently read the following quote (unfortunately, I copied it down without attribution): You may be surprised to know that Fourier analysis played a role in the early development of set theory. In ...
10GeV's user avatar
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Has Cantor's irregular enumeration of rationals ever been discussed?

Enumeration of all positive fractions recently has gained renewed interest (see the list below). By translation invariance we can be sure that in all intervals (n, n+1] of the real axis, there are the ...
Franz Kurz's user avatar
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Cantor's fortune

Wiki says that his transfinite numbers met opposition: Henri Poincaré referred to his ideas as a "grave disease" infecting the discipline of mathematics, and Leopold Kronecker's public ...
user157860's user avatar
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When did set theory throw off theology?

"The general set theory [...] definitely belongs to metaphysics. You can easily convince yourself when examining the categories of cardinal numbers and the order type, these basic notions of set ...
Franz Kurz's user avatar
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Looking for Cantor's correspondence

I am trying to collect all available letters written or received by Cantor or written between his colleagues about Cantor. I have searched already the literature given below. But I would like to ...
Franz Kurz's user avatar
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Why was Kronecker dissatisfied with Cantor's submitted paper?

It is said here that In 1874 Cantor published an article in Crelle's Journal which marks the birth of set theory. A follow-up paper was submitted by Cantor to Crelle's Journal in 1878 but already set ...
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Biography on Georg Cantor

I am looking for biographical works about Georg Cantor's life. All I have found right now are short encyclopedia-style articles that skim the important points of his life or works mainly focused on ...
Eduardo M.'s user avatar
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Kronecker vs Cantor — who won?

Now set theory is taught even to kids and it is the foundation of mathematics. Can we say that Cantor won?
ibnAbu's user avatar
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Why did Cantor (and others) use $\mathfrak{c}$ for the continuum?

Kontinuum is German for continuum, but Cantor used $\mathfrak{c}$. Revision. J.W.Perry questions whether or not Cantor ever in fact used the symbol $\mathfrak{c}$. I must admit I just assumed that he ...
Joseph O'Rourke's user avatar
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Who discovered the difference between the infinities?

As we know, there is a difference between the (infinite) size (or cardinality) of the integer numbers and the size of the reals ($\aleph_0$ and $\mathfrak c=2^{\aleph_0}$). Who discovered it first?
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Did Galileo's writings on infinity influence Cantor?

To what extent was Cantor motivated by Galileo's paradox? More generally, to what extent were late 19th century mathematicians motivated by, or even aware of, Galileo's paradox? This is an issue I've ...
Dave L Renfro's user avatar
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What motivated Cantor to invent set theory?

I can't imagine mathematics without sets, but the question "what was mathematics like before there were sets" is not answerable, I think. Instead, a good answer to the title question should cover a ...
Ben's user avatar
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