Practice Power Set Cardinality 2

harpazo

Pure Mathematics
What is the Cardinality of the Power set of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}?
 

MarkFL

La Villa Strangiato
Math Helper
\(\displaystyle P=2^{10}=1024\)

Suppose a set has a cardinality of \(n\). Then obviously, the number of subsets \(P\) that can be formed, is given by:

\(\displaystyle P=\sum_{k=0}^n\left({n \choose k}\right)=(1+1)^n=2^n\)
 

harpazo

Pure Mathematics
Interesting.
 

MarkFL

La Villa Strangiato
Math Helper
The Binomial Theorem is quite powerful. :)
 

harpazo

Pure Mathematics
Yes, it is....
 
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