Questions tagged [cantor]
Georg Ferdinand Ludwig Philipp Cantor (1845-1918) was a German mathematician who created set theory.
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What is Cantor's debt to Dedekind?
A recent article: Joseph Howlett ''The Man Who Stole Infinity'', Quanta Magazine, Feb. 25, 2026 appeared with the abstract:
Georg Cantor proved that there are different sizes of infinity and
changed ...
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I am looking for primary source quotes from Leopold Kronecker about Georg Cantor and set theory
Crossposted on Mathematics SE
I was wondering if anyone could help me find primary sources for Kronecker's criticisms. The following quote is widely found online but is never referenced. Does anyone ...
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Reference request on Georg Cantor
Georg Cantor is reported to have stated "Das Wesen der Mathematik liegt in ihrer Freiheit." Where did he state this, if at all?
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Did Gauss criticize cardinals?
In a well-known passage, Gauss criticized the use of infinity in mathematics in the following terms:
I protest first of all against the use of an infinite quantity as a completed one, which is never ...
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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 ...
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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 ...
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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 ...
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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 ...
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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
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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 ...
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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 ...