I know positive integers are 1,2,3,4,....;and the sequence of whole numbers are -3,-2,-1,0,1,2,3,...;But the Natural numbers start with one 0r zero ?
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That depends on the used convention. Some prefer $0\in\mathbb{N}$, others prefer $0\notin \mathbb{N}$. – Daniel Fischer Feb 15 '15 at 12:46
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So both of them are absolutely correct? – Norak Banges Feb 15 '15 at 12:48
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Yes, and both are absolutely wrong (from the perspective of the other convention). – Daniel Fischer Feb 15 '15 at 12:50
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It is like calling a table a table, it's just a matter of convention. You could call a horse a table, it would be another convention. Except that then, you could maybe have issues with a vast majority of people not adhering to this convention. It is really sad to see what intellectual struggle has been made to accept $0$ as an element of $\mathbf{N}$ to still see the debate on wheter $0\in\mathbf{N}$ or not. – Olórin Feb 15 '15 at 12:53
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In my country 1,2,3,4,5,....is called asli numbers,and 0,1,2,3,4,... is called cacah numbers. – Norak Banges Feb 15 '15 at 13:06
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@Robert: More like calling a horse a cheval (and those French people incorrectly do). – GEdgar Feb 15 '15 at 13:42
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@GEdgar It is not a matter of origins, but of definition, dear. For instance, you saying bull**** here is not because you are from whatever origin, but just because it is you. But I don't know if I can judge someone saying "non-decreasing"... Hum, I definitely can't. ;-) – Olórin Feb 15 '15 at 14:16