Questions tagged [cantor]

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

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4answers
2k views

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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185 views

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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1answer
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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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0answers
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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 ...
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1answer
150 views

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 ...
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4answers
1k views

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?
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3answers
501 views

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 ...
3
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2answers
420 views

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?
25
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2answers
810 views

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 ...
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3answers
3k views

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 ...