An interesting proof of inclusive-exclusive principle
七月 13, 2009 at 1:34 下午 | In Maths（数学） | Leave a CommentInclusive-Exclusive Principle (one form): There are N objects which may or may not be with property 
where 
Proof. Denote the above formula as (A), we try writing down this formula in another way. We split it as the sum of N different formulas, according to each paticular object. For an object with exact k properties, for example, we take 1 our of N to represent this object. Then note that there are exact k 
‘0′：
‘0′：
‘1′：
‘k’：$latex 1- \{k\choose 1\}+ \{k\choose 2\}-\cdots = (1-1)^k =0$
k denote the object with k different properties.
In fact, except for the first L ‘1’s, all the rest sum to zero. We can thus conclude that the formula (A) is the number of objects with not any above properties.
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