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[-] wellbuddyweek@lemm.ee 85 points 10 months ago* (last edited 10 months ago)

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

[-] yetAnotherUser@discuss.tchncs.de 67 points 10 months ago

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.

[-] wellbuddyweek@lemm.ee 8 points 10 months ago

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.

[-] Zwiebel@feddit.org 49 points 10 months ago

Natural numbers include zero

That is a divisive opinion and not actually a fact

[-] kogasa@programming.dev 5 points 10 months ago

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.

[-] SchwertImStein@lemmy.dbzer0.com 3 points 10 months ago

positive interers with addition are not a monoid though, since the identity element of addition is 0

[-] kogasa@programming.dev 3 points 10 months ago
[-] SchwertImStein@lemmy.dbzer0.com 2 points 10 months ago

I hope that explains everything

[-] davidagain@lemmy.world 2 points 10 months ago

They're not a complete algebraically closed field either, but I don't see you advocating for including e - i in the natural numbers!

[-] SchwertImStein@lemmy.dbzer0.com 1 points 10 months ago

yeah, this is kinda weak argument

[-] davidagain@lemmy.world 1 points 10 months ago

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.

[-] lengau@midwest.social 0 points 10 months ago* (last edited 10 months ago)

Yeah I find it easier to just accept the terminology of natural numbers and whole numbers so we have simple names for both.

[-] errer@lemmy.world 31 points 10 months ago

Big naturals in fact include two zeroes:

(o ) ( o)

Spaces and parens added for clarity

[-] Jerkface@lemmy.world 20 points 10 months ago* (last edited 10 months ago)

(0 ) ( 0)
You can't fool me.

[-] Quadhammer@lemmy.world 9 points 10 months ago

(o Y o) solve for Y

[-] bampop@lemmy.world 2 points 10 months ago

When enclosed in parentheses I believe the correct term is "bolt-ons"

[-] peregrin5@lemm.ee 13 points 10 months ago

Depends on how you draw it.

[-] stebo02@sopuli.xyz 1 points 10 months ago* (last edited 10 months ago)

Strictly positive numbers, Z~0~^+^, 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

[-] davidagain@lemmy.world -3 points 10 months ago

Natural numbers include zero

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.

[-] SchwertImStein@lemmy.dbzer0.com 7 points 10 months ago

american education system moment?

[-] davidagain@lemmy.world 1 points 10 months ago

I think round the world, children and adults start counting from 1. It's only natural!

[-] SchwertImStein@lemmy.dbzer0.com 2 points 10 months ago

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

[-] davidagain@lemmy.world 1 points 10 months ago

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.

this post was submitted on 04 Jun 2025
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