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
I think you’re trying to explain to me what zero means while I’m trying to explain that it’s not where numbers numbers start of from. It’s where array offsets start (but making humans make that distinction instead of compilers is on obvious own goal for language designers who weren’t intending to make off by one errors more frequent). It’s where set theory starts, but it’s absolutely not where counting starts, and number starts with counting. It’s not a natural number.
Actually, those are not the same. Natural numbers include zero, positive integers do not. She shoud definately use ‘big naturals’.
Edit: although you could argue that it doesnt matter as 0 is arguably neither big nor large
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, 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
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
Not sure if you’re conceding the monoid part or not.
We can agree that the natural numbers are a semigroup, I think, which should make us all happy.
Okay
I hope that explains everything
Yeah I find it easier to just accept the terminology of natural numbers and whole numbers so we have simple names for both.
Big naturals in fact include two zeroes:
(o ) ( o)
Spaces and parens added for clarity
(0 ) ( 0)
You can’t fool me.
(o Y o) solve for Y
When enclosed in parentheses I believe the correct term is “bolt-ons”
Depends on how you draw 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.
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
I think you’re trying to explain to me what zero means while I’m trying to explain that it’s not where numbers numbers start of from. It’s where array offsets start (but making humans make that distinction instead of compilers is on obvious own goal for language designers who weren’t intending to make off by one errors more frequent). It’s where set theory starts, but it’s absolutely not where counting starts, and number starts with counting. It’s not a natural number.
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