# PracticePower 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:

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

Interesting.

#### MarkFL

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

Yes, it is....