Content deleted Content added
→Algebraic proof: more equation linkin |
m Edited exponent in the last term of the general formula so that it's consistent with the more compact form that's given below. |
||
Line 33:
In its general form, the principle of inclusion–exclusion states that for finite sets {{math|''A''<sub>1</sub>, …, ''A<sub>n</sub>''}}, one has the identity
{{NumBlk|:|<math>\left|\bigcup_{i=1}^n A_i\right| = \sum_{i=1}^n |A_i| - \sum_{1 \leqslant i < j \leqslant n} |A_i\cap A_j| + \sum_{1 \leqslant i < j < k \leqslant n} |A_i \cap A_j\cap A_k| - \cdots + (-1)^{n
[[Image:inclusion-exclusion-3sets.png|thumb|Each term of the inclusion–exclusion formula gradually corrects the count until finally each portion of the [[Venn diagram]] is counted exactly once.]]
| |||