All Questions
Tagged with bell-numbers elementary-set-theory
4
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Calculating factorization for large numbers
My mission is to calculate the factorization of large numbers, for example, from $start=1e11$ to $end=1e12$.
To do that, one approach that I was thinking of is to calculate for each number his ...
- 119
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Constructing a bijection to show that the number of equivalence relations on a finite set is equal to the bell numbers.
It is said that the Bell numbers count the number of partitions of a finite set. How can we prove that what they count is actually the number of partitions? I don't want to take it as a definition; I ...
- 121
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Interesting ways to show that there are infinitely many equivalence relations on an infinite set (including Bell numbers).
I am trying to answer the question "Is there infinitely many equivalence relations on any infinite set?"
My intuition says yes, and when I try to prove this, I feel like my reasoning is not ...
- 131
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An $n$ element set can be written as a union of disjoint sets, in $B_n$ different ways. But what if the sets are not disjoint?
If we let $X=\{1,2,3,\ldots n\}$ then what is the value of $\left|\{\mathcal{F}\subseteq\wp(X):\bigcup\mathcal{F}=X\}\right|?$ I know that if one requires the sets in $\mathcal{F}$ be pairwise ...
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