Set Numbers and Arithmetic
Why
How does the number of elements change with unions, and products.
Results
There are a few nice relations.1 Recall from Finite Sets that the union and product of finite sets is finite. Also, the power of a finite set is finite.
Let $A$ and $B$ be finite sets with $A \cap
B = \varnothing$.
Then $\num{A \cup B} = \num{A} + \num{B}$.
Let $A$ and $B$ be a finite sets
Then $\num{A \times B} = \num{A} \cdot
\num{B}$.
Let $A$ and $B$ be a finite sets
Then $\num{A^B} = \num{A}^{\num{B}}$.
Let $A$ be a finite set.
Then $\num{\powerset{A}} = 2^{\nu m{A}}$.
- Proofs will appear in future editions. ↩︎