Linked Questions
4 questions linked to/from Cardinality of the permutations of an infinite set
75
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When the automorphism group of an object determines the object
Let me start with three examples to illustrate my question (probably vague; I apologize in advance).
$\mathbf{Man}$, the category of closed (compact without boundary) topological manifold. For any $M,...
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7
answers
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Easy proof of the uncountability of bijections on natural numbers
Is there an easy proof of the uncountability of bijections on natural numbers?
The proof that I have in mind is as follows -
$\text{Gal }(\overline{\mathbb Q}/\mathbb Q)$ is a proper uncountable ...
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2
answers
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Terminology for a bijection from a set to itself
A current project uses bijections from a set to itself. (The set is the integer compositions of $n$, i.e., "ordered partitions of $n$," but that doesn't seem pertinent to the question.) Is ...
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Cardinality of symmetric group [duplicate]
Possible Duplicate:
Cardinality of the permutations of an infinite set
Why does the symmetric group on an infinite set X have the cardinality of the power set ${\cal P}(X)$?
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