Suppose that you have a set A with n elements. Is there a closed form solution of the number of ways that A can be partitioned in terms of n?

As an example, consider A = {a,b,c}. Then there are 5 different ways to partition this set.

1. a~a b~b c~c

2. a~b c~c

3. a~a b~c

4. a~c b~b

5. a~b~c

So I am trying to come up with some general formula for this. Even easier, there are 2 ways to partition a set with 2 elements, and only 1 way to partition a 1 element set.

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## Comments

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TopNewestI think you are referring to the Bell numbers:

https://en.wikipedia.org/wiki/Bell_number

http://mathworld.wolfram.com/BellNumber.html

And if I understand correctly, there are only 2 ways to partition a set with two elements.

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Thank you. I rushed in typing the last sentence, but I will edit that. Thank you! You found exactly what I was looking for.

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