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Zero: Natural or Counting Number?

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nycfunction

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May 24, 2019
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Zero is an integer. An integer is defined as all positive and negative whole numbers and zero. Zero is also a whole number, a rational number and a real number, but it is not typically considered a natural number, nor is it an irrational number. Why is 0 not a natural or counting number?
 

HallsofIvy

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MHB Math Helper
Jan 29, 2012
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You realize, I hope, that this is simply a convention. The "counting numbers" (also called the "natural numbers") are defined as the positive whole numbers. If you really want a reason, I would offer that you start counting things "1, 2, 3, …", not "0, 1, 2, 3, …".
 

Klaas van Aarsen

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Mar 5, 2012
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What HallsofIvy said ^^.

Also, the definition of natural numbers is not universally consistent. Some conventions include 0. Others exclude 0.
It means we have to be careful with natural numbers, and always check how an author defines them.
Best IMHO is to avoid the phrase natural numbers altogether, since it's a source of ambiguity and confusion.
 
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nycfunction

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May 24, 2019
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What HallsofIvy said ^^.

Also, the definition of natural numbers is not universally consistent. Some conventions include 0. Others exclude 0.
It means we have to be careful with natural numbers, and always check how an author defines them.
Best IMHO is to avoid the phrase natural numbers altogether, since it's a source of ambiguity and confusion.
Why is the phrase NATURAL NUMBERS ambiguous and confusing?
 

topsquark

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Aug 30, 2012
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Evgeny.Makarov

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Jan 30, 2012
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If you really want a reason, I would offer that you start counting things "1, 2, 3, …", not "0, 1, 2, 3, …".
The mathematician S. had to move to a new place. His wife didn't trust him very much, so when they stood down on the street with all their things, she asked him to watch their ten trunks, while she get a taxi. Some minutes later she returned. Said the husband:
"I thought you said there were ten trunks, but I've only counted to nine."
The wife said: "No, they're TEN!"
"But I have counted them: 0, 1, 2, ..."
From here.
 
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nycfunction

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May 24, 2019
13
The mathematician S. had to move to a new place. His wife didn't trust him very much, so when they stood down on the street with all their things, she asked him to watch their ten trunks, while she get a taxi. Some minutes later she returned. Said the husband:
"I thought you said there were ten trunks, but I've only counted to nine."
The wife said: "No, they're TEN!"
"But I have counted them: 0, 1, 2, ..."
From here.
When we count things, zero must be excluded. Zero is never assigned to items or people when we count. I get it now. It should have been obvious to me.

However, I have seen a few major league baseball players in MLB history assigned the number 0 on the back of the uniform shirt. If memory serves me right, I think one baseball player in baseball history was assigned a DOUBLE ZERO on the back of his uniform shirt.