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So it is not a right if exercising the "right" would conflict with another person's similar exercising of his right?
You are mistaken. A quick example: You have the right to express your thoughts, but you do not have the right to enter into my home to do so without my permission. Your right is restricted when it would violate one of my rights. By denying you entrance into my home, I have not infringed upon your right to express your thoughts.
Yours,
Issodhos