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Section8.7Discussion

After studying the proof that the number of partitions of an integer into odd parts is the same as the number of partitions of that integer into distinct parts, Yolanda was beside herself. “Do you guys realize what we just did? We showed that two quantities were equal without saying anything about what those quantities actually were. That's really neat,” she said. Nobody said anything for a long time, but after some time Dave said “There might be other instances where you would want to be able to communicate fully, yet hold back on every last detail.” Bob said “I don't get it.” Alice interjected a comment that was more of question than a statement “Do you mean that parties may want to communicate, while maintaining that the conversation did not occur?” Carlos added “Or maybe they just want to be able to detect whether anyone else was listening.” Now Zori was nearly happy. Privacy and security were big ticket items.