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I have thought about this for a long time, since I have done some Grade 8 American Math League (A Competition) Past Papers, but when it asked some question like: How many whole numbers have their square less than or equal to $200$, I thought any integer from $-14$ to $14$ works, which is $29$ whole numbers, but the answer says there are only $15$. I then searched up the definition of whole numbers, and most of the sites said they were nonnegative integers, while others just say a whole number is any integer.

But if a whole number is a nonnegative integer, then why do questions like "Round $-3.6$ to the nearest whole number" exist?

I've discussed this question with my teacher and even the Head of Mathematics of my school, but they both said that a whole number is any integer. My maths teacher also said that we only would talk about integers and not whole numbers in High School, but I am still curious about what a whole number actually is.

Thank you very much!

Cornman
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Cheese Cake
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    A whole number is an element of $\mathbb{Z}={0,\pm 1, \pm 2,\dotso}$. So nothing special here. I would guess that the solution in the answer is just a typo. – Cornman Mar 14 '22 at 08:18
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    The question about squares less than 200 should/could have specified the range of possible solutions: positive, non-negative etc. – Peter Phipps Mar 14 '22 at 08:20
  • Thank you, but I think in most websites, it states that it is a nonnegative number, so I am not exactly sure about this. One website is: https://www.mathsisfun.com/definitions/whole-number.html – Cheese Cake Mar 14 '22 at 08:20
  • True, it just said "whole numbers" – Cheese Cake Mar 14 '22 at 08:20
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    I also think that the term "whole number" is never really defined. The common way is to talk about integers in the english language. As a native german I would say "ganze Zahl" (whole number). So I think that the term originated from the german. That is where the notation $\mathbb{Z}$ from Zahl (=number) come from. So it might be more or less just a way of communicating. A synonym for integer. – Cornman Mar 14 '22 at 08:21
  • Thank you Cornman! – Cheese Cake Mar 14 '22 at 08:22
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    @CheeseCake "Whole number" is whatever it was defined to be in the context you are working in, nothing more and nothing less. It does not have a rigorous, universally accepted definition. See for example wikipedia: "the meaning is ambiguous. It may refer to either...". – dxiv Mar 14 '22 at 08:22
  • True, I saw that and forgot to mention it – Cheese Cake Mar 14 '22 at 08:23
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    @CheeseCake I do not think that the website "mathisfun.org" is a reliable source. I can not recollect a single time where a "whole number" was defined in a textbook. – Cornman Mar 14 '22 at 08:23
  • @Cornman I'm not sure if the link I attached below is a textbook, but it is defined as a nonnegative integer in an indirect way. http://www.opentextbookstore.com/arithmetic/book.pdf – Cheese Cake Mar 14 '22 at 08:25
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    @dxiv, I think your comment would be good as an answer. – Mees de Vries Mar 14 '22 at 08:25
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    @CheeseCake Might be. Keep in mind that for some authors we have $\mathbb{N}={0,1,\dotso}$. Others let $\mathbb{N}={1,2,\dotso}$. Stuff like this exists a lot in mathematics. It is as dxiv says. Probably in context of the competition a "whole number" was defined. – Cornman Mar 14 '22 at 08:27
  • @Cornman That is true, as in Australia we have natural numbers as positive integers, and PROBABLY whole numbers as all integers. – Cheese Cake Mar 14 '22 at 08:33
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    @MeesdeVries There have been several helpful comments for the OP to draw their own conclusion, and perhaps post it as a self-answer. – dxiv Mar 14 '22 at 08:34
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    A whole number doesn't have any pieces left over like fractions. This is really a question for Sesame Street. – John Douma Mar 14 '22 at 09:34
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    The definition of an integer is not ambigous. And usually, a whole number is nothing else than an integer. If natural numbers (with or without $0$) or nonnegative whole numbers are meant, it would be better to state this explicite. Whether $0$ belongs to the natural number is another story. There seems to be no convention about this. – Peter Mar 14 '22 at 10:43
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    Honestly, this is the first time I've ever heard that a "whole number" might be negative. I'd thought it always meant "nonnegative integer". – Mark S. Mar 14 '22 at 13:02
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    I was sure that "whole numbers" and integers are synonyms. Until this discussion Why don’t American school textbooks recognize negative numbers as whole numbers?, where I learnt that there is no such consensus. Now I just avoid using this phrase. – ryang Mar 14 '22 at 13:51

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After several days, I saw that in the Australian Textbook Year 11 Extension 1 Chapter 2A that whole numbers are nonnegative integers.

Thank you for your help!

Cheese Cake
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