Natural numbers only include zero if you define it so in the beginning of your book/paper/whatever. Otherwise it’s ambiguous and you should be ashamed of yourself.
Fair enough, as a computer scientist I got tought to use the Neumann definition, which includes zero, unless stated differently by the author. But for general mathematics, I guess it’s used both ways.
Yeah, it’s a matter of convention rather than opinion really, but among US academia the convention is to exclude 0 from the naturals. I think in France they include it.
Only if you’re French or a computer scientist or something! No one else counts from zero.
There’s nothing natural about zero. The famously organized and inventive Roman Empire did fine without it and it wasn’t a popular concept in Europe until the early thirteenth century.
If zero were natural like 1, 2, 3, 4, then all cultures would have counted from zero, but they absolutely did not.
I think about this in terms can I have of something (indivisible), and sure enough I can have 0 apples (yeah, yeah, divisible), bruises, grains of sand in my pocket
Actually, those are not the same. Natural numbers include zero, positive integers do not. She shoud definately use ‘big naturals’.
Depends on how you draw it.
Natural numbers only include zero if you define it so in the beginning of your book/paper/whatever. Otherwise it’s ambiguous and you should be ashamed of yourself.
Fair enough, as a computer scientist I got tought to use the Neumann definition, which includes zero, unless stated differently by the author. But for general mathematics, I guess it’s used both ways.
That is a divisive opinion and not actually a fact
Yeah I find it easier to just accept the terminology of natural numbers and whole numbers so we have simple names for both.
Yeah, it’s a matter of convention rather than opinion really, but among US academia the convention is to exclude 0 from the naturals. I think in France they include it.
positive interers with addition are not a monoid though, since the identity element of addition is 0
Okay
I hope that explains everything
They’re not a complete algebraically closed field either, but I don’t see you advocating for including e - i in the natural numbers!
yeah, this is kinda weak argument
Big naturals in fact include two zeroes:
(o ) ( o)
Spaces and parens added for clarity
(o Y o) solve for Y
(0 ) ( 0)
You can’t fool me.
Strictly positive numbers, Z0+, don’t include zero. Positive numbers aka naturals, Z+ = N, do.
Edit: this is what I’ve learned at school, but according to wikipedia the definitions of these vary quite a bit
Only if you’re French or a computer scientist or something! No one else counts from zero.
There’s nothing natural about zero. The famously organized and inventive Roman Empire did fine without it and it wasn’t a popular concept in Europe until the early thirteenth century.
If zero were natural like 1, 2, 3, 4, then all cultures would have counted from zero, but they absolutely did not.
american education system moment?
I think round the world, children and adults start counting from 1. It’s only natural!
I think about this in terms can I have of something (indivisible), and sure enough I can have 0 apples (yeah, yeah, divisible), bruises, grains of sand in my pocket