# Is this a correct way to describe number sets?

And they shouldn't. ##0## is a human achievement and nothing natural.
I also agree to this viewpoint

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.

fresh_42
Mentor
You think Graham's number is natural?
Hmm, I'd rather say funny. In any case it's a nice example how to code something huge in a small number of digits.

Did we invent the numbers? or discover them?

Did we invent the numbers? or discover them?
Meh, once you rigorously define those terms, we might find an answer. So far, nobody has really given a satisfactory definition.

Logical Dog
fresh_42
Mentor
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.

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

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.

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

fresh_42
Mentor
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
Mentor
Compromise:

Include 0 only half. Is that natural enough?

Math_QED and S.G. Janssens
fresh_42
Mentor
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 ....

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