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Now, Nimz, this is where you've got it wrong. Some people do include 0 as a natural number, some people do not. Some people define 0 to be positive and negative and use the phrases strictly positive and strictly negative to exclude it. Others take it to be neither and use the phrase non-negative to mean 0,1,2... It is all a matter of what your conventions are. You have assumed that yours are absolutely correct, and that is not the case.
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