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Jan 19, 2012 at 20:09 vote accept Incognito
Jan 19, 2012 at 19:45 comment added Will Orrick The binary pattern can be identified with the indicator function, $\mathbf{1}_S$ of the set $S$. If you scroll down to the section Basic properties in the Wikipedia article linked to above, you will see a form of the Principle of Inclusion-Exclusion expressed using indicator functions.
Jan 19, 2012 at 15:39 comment added Incognito Re: "I'm not sure whether this is what you're getting a". I suppose what I want to express is that we can generate all of the sets in that binary-pattern way, and that the bit-population being even or odd determines if we add or subtract the term.
Jan 19, 2012 at 2:48 history answered Will Orrick CC BY-SA 3.0