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nycfunction

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In summary: I get it now. It should have been obvious to me. 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. Zero is not a natural number because it is not assigned to items or people when we count. It is clear now, isn't it?

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nycfunction

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Mathematics news on Phys.org

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HallsofIvy

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I like Serena

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Also, the definition of

It means we have to be careful with

Best IMHO is to avoid the phrase

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nycfunction

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Klaas van Aarsen said:

Also, the definition ofnatural numbersis not universally consistent. Some conventions include 0. Others exclude 0.

It means we have to be careful withnatural numbers, and always check how an author defines them.

Best IMHO is to avoid the phrasenatural numbersaltogether, since it's a source of ambiguity and confusion.

Why is the phrase NATURAL NUMBERS ambiguous and confusing?

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nycfunction said:Why is the phrase NATURAL NUMBERS ambiguous and confusing?

Klaas van Aarsen said:What HallsofIvy said ^^.

Also, the definition ofnatural numbersis not universally consistent. Some conventions include 0. Others exclude 0.

If sources define the same term with different definitions then there will be confusion. It's nothing more than that.

-Dan

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Evgeny.Makarov

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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:HallsofIvy said:If you really want a reason, I would offer that you start counting things "1, 2, 3, …", not "0, 1, 2, 3, …".

"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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Evgeny.Makarov said: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.

Yes, zero is considered a natural number. It is defined as a non-negative integer and is included in the set of natural numbers (0, 1, 2, 3...).

Yes, zero can be used as a counting number. It is often used to represent the absence of a quantity or to indicate an empty set.

Zero is considered an even number. This is because it is divisible by 2 and leaves no remainder.

The concept of zero has been around for thousands of years, but it was first used as a number in the ancient Indian civilization. It was later adopted by other civilizations, including the Greeks and Romans.

Zero plays a crucial role in mathematics, as it is used as a placeholder in our number system and allows us to represent numbers of any magnitude. It is also essential in algebra, calculus, and other branches of mathematics.

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