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### Round-robin party presents (or: Graeco-Latin square with additional cycle property)

A group of $n$ people organizes recurring parties, $n-1$ events in total. At each event, each person offers a present to one other person, and each person receives a present ($n$ presents exchanged in ...
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### A setting in which Rice's theorem is not true

In my class we call a set of computable functions $A$ recursive if its indexing set $I_A=\{e\in\mathbb N:\phi_e\in A \}$ is recursive, where $\phi$ is some known Gödel numbering of the computable ...
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### Expected number of tosses to get T,T

Assume a coin has a probability p to get a head H. Suppose a coin is tossed until the partern T,T appear in the last 2 tosses. Once he got T,T then the game is finished. What is the expected number of ...
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Russell's paradox is about a set not in a set itself - but don't all sets are not in sets themselves? $x \in x$ is not true, as {$1,2,3$} $\in$ {$1,2,3$} is not true.. Can anyone explain this?
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### Examples of results failing in higher dimensions

A number of economists do not appreciate rigor in their usage of mathematics and I find it very discouraging. One of the examples of rigor-lacking approach are proofs done via graphs or pictures ...