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#### MI5

##### New member

- Sep 8, 2013

- 8

$ |A| = \sum_{i=1}^{n}|A_i|$. (1)

Proof: According to the hypothesis, each $a \in A$ belongs to exactly one of the subsets $A_{i}$,

**and therefore it counts exactly once on each side of equation 1.**

Could someone explain the bold bit (what's meant by it counts exactly once on each side of the equation) and why that counts as proof.