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Results tagged with axiom-of-choice
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user 15570
An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually disjoint nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets. The axiom of choice is related to the first of Hilbert's problems.
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Can a weaker version of the Hausdorff paradox be proved without AC?
The Hausdorff paradox is an incredibly counter-intuitive consequence of the axiom of choice; it is also important for demonstrating the non-existence, under AC, of a rotation-invariant measure on the …
- 708
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Can a weaker version of the Hausdorff paradox be proved without AC?
Following the suggestion in the first comment below my question (and with the help of the second comment), I can give an example of a scenario that is "even worse" than what I requested, where $A \cup …
- 708