Is this a correct way to describe number sets?

[fresh_42]

But sure, $0$ is unnatural. I have 2 apples and give 2 apples to my brother. What I have left is nothing natural??

Also, axiomatic set theory is pretty clear on the issue that $0$ should be a natural number. You'd make a mess out of the theory otherwise.

But this argument is essentially practicability as it is to exclude units to be prime. I have no problem when people work with $\mathbb{N}_0$ though.

 

[Logical Dog]

Meh, once you rigorously define those terms, we might find an answer. So far, nobody has really given a satisfactory definition.

ok boss..this is all way over my head. xD

 

[micromass]

But this argument is essentially practicability as it is to exclude units to be prime. I have no problem when people work with $\mathbb{N}_0$ though.

Well, clearly you don't think math should be elegant. I think elegance trumps everything else. And if you believe in elegance, $0$ should be a natural.

 

[Logical Dog]

number is undefined, so is point, proposition, true, false, set, element...

 

[fresh_42]

Well, clearly you don't think math should be elegant. I think elegance trumps everything else. And if you believe in elegance, $0$ should be a natural.

Oh no. I won't turn into this ... Far too obvious!

 

[mfb]

Compromise:

Include 0 only half. Is that natural enough?

 

[fresh_42]

Compromise:

View attachment 106007

Include 0 only half. Is that natural enough?

We have to ask the Indians. As far as I know they have the copyright on the $0$. I'm sure we've had numbers when we lived in Africa, but it took a civilization to use the $0$. Probably some bookies ...

 

[micromass]

We have to ask the Indians. As far as I know they have the copyright on the $0$. I'm sure we've had numbers when we lived in Africa, but it took a civilization to use the $0$. Probably some bookies ...

Some tribes count as $1,2,3,\text{many}$. So I deny that the number $10$ is very natural.

 

[jbriggs444]

Some tribes count as $1,2,3,\text{many}$. So I deny that the number $10$ is very natural.

It's just another name for 2.