# Mathematical Dopers: Does the set of the naturals include zero?

**URL:** <https://boards.straightdope.com/t/mathematical-dopers-does-the-set-of-the-naturals-include-zero/569764>\
**Category:** In My Humble Opinion\
**Created:** [February 1, 2011, 7:46am UTC](https://boards.straightdope.com/t/mathematical-dopers-does-the-set-of-the-naturals-include-zero/569764 "2011-02-01T07:46:22Z")\
**Posts on this page:** 4\
**Page:** 3

<div class="post-metadata">

**Author:** ![The\_wind\_of\_my\_soul](https://avatars.discourse-cdn.com/v4/letter/t/ecc23a/32.png) [@The\_wind\_of\_my\_soul](https://boards.straightdope.com/u/The_wind_of_my_soul)\
**Post date:** [February 8, 2011, 7:47pm UTC](https://boards.straightdope.com/t/mathematical-dopers-does-the-set-of-the-naturals-include-zero/569764/41 "2011-02-08T19:47:27Z")

</div>

I’m surprised by this lack of consensus. I didn’t vote in this poll because it’s possible that I’m just remembering things wrong. But my dad and brother are both mathematicians (the kind that pursued higher degrees in the subject and read books on complex mathematical theories for fun), and they used to say “Zero is a real number; it is not a natural number” with such certainty that I had always thought this was universally accepted. (And if anyone said otherwise, I was sure they were wrong, because the person who got a doctorate in mathematics surely knew best.)

---

<div class="post-metadata">

**Author:** ![Jamaika\_a\_jamaikaiake](https://avatars.discourse-cdn.com/v4/letter/j/7993a0/32.png) [@Jamaika\_a\_jamaikaiake](https://boards.straightdope.com/u/Jamaika_a_jamaikaiake)\
**Post date:** [February 8, 2011, 9:07pm UTC](https://boards.straightdope.com/t/mathematical-dopers-does-the-set-of-the-naturals-include-zero/569764/42 "2011-02-08T21:07:15Z")

</div>

> [@Thudlow\_Boink](#):
>
> Zorn’s Lemon

What’s green and has integer coordinates?

or

What’s green and has 2 coordinates?

---

<div class="post-metadata">

**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\
**Post date:** [February 8, 2011, 9:27pm UTC](https://boards.straightdope.com/t/mathematical-dopers-does-the-set-of-the-naturals-include-zero/569764/43 "2011-02-08T21:27:52Z")

</div>

In my college (in Switzerland), we used this notation:  
N = { 0, 1, 2, … }  
N\* = { 1, 2, 3, … }  
Z = { … -3, -2, -1, 0, 1, 2, … }

---

<div class="post-metadata">

**Author:** ![Jamaika\_a\_jamaikaiake](https://avatars.discourse-cdn.com/v4/letter/j/7993a0/32.png) [@Jamaika\_a\_jamaikaiake](https://boards.straightdope.com/u/Jamaika_a_jamaikaiake)\
**Post date:** [February 9, 2011, 3:02pm UTC](https://boards.straightdope.com/t/mathematical-dopers-does-the-set-of-the-naturals-include-zero/569764/44 "2011-02-09T15:02:42Z")

</div>

> [@Arnold\_Winkelried](#):
>
> In my college (in Switzerland), we used this notation:  
> N = { 0, 1, 2, … }  
> N\* = { 1, 2, 3, … }  
> Z = { … -3, -2, -1, 0, 1, 2, … }

I’ve seen this, as well. However, in some contexts, N\* can mean the naturals with the reverse ordering: …, 3, 2, 1, 0.

[Previous page](https://boards.straightdope.com/t/mathematical-dopers-does-the-set-of-the-naturals-include-zero/569764.md?page=2)