/sci/ - Science & Math

But that isn't right.

>>2641853
>>2641853
>>2641853

How is it not right? It's a fairly standard relationship in set theory

>>2641890
No, it's right (though your notation for exponentiation is nonstandard). Consider. The power set is the set of all subsets. So consider a set of cardinality n. Each subset must make a choice {yes, no} with regard to each element. So the number of subsets is the number of ways to make all of these choices: 2x2x...x2 (string length=n). This is 2^n.

>>2641921
>>2641921
>>2641921

You're right, when I pasted this problem in it didn't keep the exponent, sorry about that. You answer sounds correct, but it isn't completely clear. Why did you assume 2x2x2x...x2?

>>2641928
Each element must be chosen either yes or no (2 choices) for each subset (n times). Choose yes or no for the first element and that divides the subsets into 2 groups (those with and those without the first element). Then those groups are each divided into 2 groups for the second element (those with and those without the second element). Thus the size of the set of subsets doubles each time you choose with respect to an element. By the time you've chosen for all the elements, the set of subsets has doubled n times.

>>2641941
>>2641941

Ah, I understand now. Thank you so much, this wasn't actually on a test, it's on a homework assignment that is due in 20 minutes. Most of the time people aren't willing to help, so I have to disguise my question.

THANKYOU!

>>2641969
Philosophy=love of knowledge

>>2641847
>mfw it's n
I thought it was omega, for some reason..
for n it's trivial. just put 'trivial' at the excercise