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**teineg****Member**- Registered: 2008-09-08
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Why is a set of factor of a number not the same as the set of proper factor of that number

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

A proper factor of a number is not allowed to be 1 or the number itself, but a factor can be.

For example, the factors of 6 are 1, 2, 3, 6, but its proper factors are only 2 and 3.

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It wanted to be normal.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
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But rather strangely there is disagreement on whether 1 should be included or not.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
- Posts: 782

MathsIsFun wrote:

But rather strangely there is disagreement on whether 1 should be included or not.

Like the disagreement on whether 0 should be integer or not?

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**greg1313****Member**- Registered: 2016-12-19
- Posts: 14

Monox D. I-Fly wrote:

MathsIsFun wrote:But rather strangely there is disagreement on whether 1 should be included or not.

Like the disagreement on whether 0 should be integer or not?

There's no disagreement I know of about whether 0 should be an integer or not.

There's inconsistency of whether 0 is a called a counting number or not.

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
- Posts: 782

As far as I know:

Natural numbers = 1, 2, 3, and so on.

Integers = 0, 1, 2, 3, and so on.

But many people disagree.

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The natural numbers, denoted by , are usually given as the infinite set . Some authors take it to include the number , and to mark this distinction, they often write this as or the more explicit . Authors usually make it clear what they want to mean by 'natural number'. However, I have never come across any ambiguity over the use of the word 'integer' -- denoted by , it always describes the set in the modern usage of the word, unless you have seen otherwise?

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
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What I have seen:

1, 2, 3, and so on = natural numbers

0, 1, 2, 3, and so on = integers

..., -3, -2, -1, 0, 1, 2, 3, ... = whole numbers

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Where did you see that?

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
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It's just how Indonesians translate them.

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 659

Monox D. I-Fly wrote:

What I have seen:

1, 2, 3, and so on = natural numbers

0, 1, 2, 3, and so on = integers

..., -3, -2, -1, 0, 1, 2, 3, ... = whole numbers

Sorry, but you interchanged whole numbers and integers.

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
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It's just translation problem.

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