# Questions tagged [set-theory]

For questions about the mathematical branch that is based on the study of sets, i.e. collections of objects.

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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 ...
1 vote
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### History of exponential notation for the set of functions between two sets

It's well-known that if $A$ and $B$ are two sets, then the set of all functions from $A$ to $B$ can be denoted by $B^A$: explanations of this particular notation can be found in many places: https://...
602 views

### Were transcendental numbers considered rare, pre-Cantor?

Because the real numbers are uncountable and the real algebraic numbers are countable, there are uncountably many transcendental numbers. So there are far more transcendentals than rationals. With the ...
303 views

### Was the continuum hypothesis commonly believed to be independent before Cohen's proof?

Someone drew my attention to the Russian translation of Rademacher and Toeplitz's Von Zahlen und Figuren (The Enjoyment of Mathematics in the English translation). In the chapter on set theory the ...
158 views

### Who decided on the convention for ordinal multiplication?

Ordinal multiplication has always seemed backwards to me. $\alpha \times \beta$ is defined as the concatenation of $\beta$ copies of $\alpha$, not the other way 'round as one might expect. Does this ...
109 views

### Lengths as equivalence classes

From Wikipedia on cardinal numbers: The oldest definition of the cardinality of a set $X$ (implicit in Cantor and explicit in Frege and Principia Mathematica) is as the class $[X]$ of all sets ...
334 views

### Can we identify Paul Benacerraf in these photos

This question is about Paul Benacerraf, who worked on the philosophy of mathematics, and wrote the 1965 essay What numbers could not be (see: Benacerraf's identification problem). He was at Princeton ...
280 views

### Was Paul Cohen a student or assistant of Gödel?

In The Man Who Loved Only Numbers, a biography about Paul Erdős, by Paul Hoffman, the author claims that Paul Cohen was "Gödel's former assistant" (p 225). However, I can't find any other sources ...
246 views

### Who was (were) the first mathematician(s) who did not doubt the empty set?

Today there is no doubt that the empty set for the whole of mathematics is as reasonable and useful as zero for arithmetic. This however was not always the case, and surprisingly even Zermelo, who ...
156 views

### Did Zermelo in 1914 miss the fact that there are only countably many finite strings?

Did Zermelo in 1914 miss the fact, known in 1905 already, that there are only countably many finite strings, for instance polynomials with defined parameters? He wrote: Every real or complex number \$\...
220 views

### Endorsers of the method of well-ordering reported by Hausdorff?

In the course of preparing a lecture for graduate students about errors of early set theory I have come across this nice example reported by Hausdorff which violates Peano's successor axiom but ...