# of different binary ops. on a set S

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The discussion centers on the number of distinct binary operations that can be defined on a set S with varying numbers of elements. The consensus is that for a set with 1 element, there is 1 binary operation; for 2 elements, there are 2^4 (16) operations; for 3 elements, the total is 3^9 (19683); and for n elements, the formula is n^(n^2). This conclusion is reached through the understanding of combinations and assignments of values to pairs within the set.

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Unassuming
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Bear with me,

Haow mainy difffferent biiinary operarations can be dephined on the set S when it has 1,2,3 or n elementz?

Sorry I typed so weird, I don't want anybody finding this answer.

Can I confirm with you guys/gals in here that the answer is (hopefully)

1 elem = 1,
2 elem = 2^4
3 elem = 3^9
n elem = n^(n^2)

I have never had any combo class so forgive me if I am wrong with this.
 
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Hi Unassuming! :smile:

hmm … never come across that before …

if the question means what I think it does, then I agree with you …

there are n values to be assigned to n² combinations, so it's n^n². :smile:

(I think … :rolleyes:)
 

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