this post was submitted on 07 May 2024
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[–] expr@programming.dev 87 points 6 months ago (2 children)

I just found out about this debate and it's patently absurd. The ISO 80000-2 standard defines ℕ as including 0 and it's foundational in basically all of mathematics and computer science. Excluding 0 is a fringe position and shouldn't be taken seriously.

[–] RandomWalker@lemmy.world 38 points 6 months ago (11 children)

I could be completely wrong, but I doubt any of my (US) professors would reference an ISO definition, and may not even know it exists. Mathematicians in my experience are far less concerned about the terminology or symbols used to describe something as long as they’re clearly defined. In fact, they’ll probably make up their own symbology just because it’s slightly more convenient for their proof.

[–] doctordevice@lemmy.ca 19 points 6 months ago* (last edited 6 months ago)

My experience (bachelor's in math and physics, but I went into physics) is that if you want to be clear about including zero or not you add a subscript or superscript to specify. For non-negative integers you add a subscript zero (ℕ_0). For strictly positive natural numbers you can either do ℕ_1 or ℕ^+.

[–] Emmie@lemm.ee 11 points 6 months ago* (last edited 6 months ago)

I hate those guys. I had that one prof at uni and he reinvented every possible symbol and everything was so different. It was a pita to learn from external material.

[–] Leate_Wonceslace@lemmy.dbzer0.com 8 points 6 months ago* (last edited 6 months ago)

they’ll probably make up their own symbology just because it’s slightly more convenient for their proof

I feel so thoroughly called out RN. 😂

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[–] kogasa@programming.dev 9 points 6 months ago* (last edited 6 months ago) (9 children)

Ehh, among American academic mathematicians, including 0 is the fringe position. It's not a "debate," it's just a different convention. There are numerous ISO standards which would be highly unusual in American academia.

FWIW I was taught that the inclusion of 0 is a French tradition.

[–] Leate_Wonceslace@lemmy.dbzer0.com 7 points 6 months ago* (last edited 6 months ago) (3 children)

I'm an American mathematician, and I've never experienced a situation where 0 being an element of the Naturals was called out. It's less ubiquitous than I'd like it to be, but at worst they're considered equally viable conventions of notation or else undecided.

I've always used N to indicate the naturals including 0, and that's what was taught to me in my foundations class.

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[–] dogsoahC@lemm.ee 73 points 6 months ago (5 children)

Well, you can naturally have zero of something. In fact, you have zero of most things right now.

[–] AnUnusualRelic@lemmy.world 42 points 6 months ago

How do you know so much about my life?

[–] tate@lemmy.sdf.org 6 points 6 months ago (4 children)

But there are an infinite number of things that you don't have any of, so if you count them all together the number is actually not zero (because zero times infinity is undefined).

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[–] affiliate@lemmy.world 26 points 6 months ago* (last edited 6 months ago) (1 children)

the standard (set theoretic) construction of the natural numbers starts with 0 (the empty set) and then builds up the other numbers from there. so to me it seems “natural” to include it in the set of natural numbers.

On top of that, I don't think it's particularly useful to have 2 different easy shorthands for the positive integers, when it means that referring to the union of the positive integers and the singleton of 0 becomes cumbersome as a result.

[–] ns1@feddit.uk 23 points 6 months ago (3 children)

Counterpoint: if you say you have a number of things, you have at least two things, so maybe 1 is not a number either. (I'm going to run away and hide now)

[–] Kusimulkku@lemm.ee 10 points 6 months ago (1 children)

"I have a number of things and that number is 1"

[–] assa123@lemmy.dbzer0.com 6 points 6 months ago (1 children)

I have a number of friends and that number is 0

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[–] JDubbleu@programming.dev 7 points 6 months ago

I'm willing to die on this hill with you because I find it hilarious

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[–] baseless_discourse@mander.xyz 19 points 6 months ago* (last edited 6 months ago)

I think if you ask any mathematician (or any academic that uses math professionally, for that matter), 0 is a natural number.

There is nothing natural about not having an additive identity in your semiring.

[–] RandomVideos@programming.dev 12 points 6 months ago (2 children)

In school i was taught that ℕ contained 0 and ℕ* was ℕ without 0

[–] Faresh@lemmy.ml 13 points 6 months ago (1 children)

I was taught ℕ did not contain 0 and that ℕ₀ is ℕ with 0.

[–] Eylrid@lemmy.world 15 points 6 months ago

ℕ₀* is ℕ with 0 without 0

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[–] Allero@lemmy.today 10 points 6 months ago (4 children)

Why do we even use natural numbers as a subset?

There are whole numbers already

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[–] CodexArcanum@lemmy.world 10 points 6 months ago (3 children)

I'd learned somewhere along the line that Natural numbers (that is, the set ℕ) are all the positive integers and zero. Without zero, I was told this were the Whole numbers. I see on wikipedia (as I was digging up that Unicode symbol) that this is contested now. Seems very silly.

[–] MBM@lemmings.world 8 points 6 months ago (3 children)

I think whole numbers don't really exist outside of US high schools. Never learnt about them or seen them in a book/paper at least.

[–] CodexArcanum@lemmy.world 6 points 6 months ago

I wouldn't be surprised. I also went to school in MS and LA so being taught math poorly is the least of my educational issues. At least the Natural numbers (probably) never enslaved anyone and then claimed it was really about heritage and tradition.

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[–] pooberbee@lemmy.ml 10 points 6 months ago (2 children)

It is a natural number. Is there an argument for it not being so?

[–] jroid8@lemmy.world 21 points 6 months ago (2 children)
[–] darthelmet@lemmy.world 21 points 6 months ago

Well I’m convinced. That was a surprisingly well reasoned video.

[–] Sorse@discuss.tchncs.de 7 points 6 months ago

Thanks for linking this video! It lays out all of the facts nicely, so you can come to your own decision

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[–] l10lin@lemmy.world 9 points 6 months ago (2 children)

Definition of natural numbers is the same as non-negative numbers, so of course 0 is a natural number.

[–] blind3rdeye@lemm.ee 12 points 6 months ago* (last edited 6 months ago)

In some countries, zero is neither positive nor negative. But in others, it is both positive and negative. So saying the set of natural number is the same as non-negative [integers] doesn't really help. (Also, obviously not everyone would even agree that with that definition regardless of whether zero is negative.)

[–] dovahking@lemmy.world 7 points 6 months ago

But -0 is also 0, so it can't be natural number.

[–] NoFood4u@sopuli.xyz 9 points 6 months ago

I like how whenever there's a pedantic viral math "problem" half of the replies are just worshiping one answer blindly because that's how their school happened to teach it.

[–] AppleMango@lemmy.world 8 points 6 months ago (1 children)

I have been taught and everyone around me accepts that Natural numbers start from 1 and Whole numbers start from 0

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[–] Sam_Bass@lemmy.world 8 points 6 months ago
[–] Toes@ani.social 8 points 6 months ago

Negative Zero stole my heart

[–] SuperSpruce@lemmy.zip 7 points 6 months ago (2 children)

0 is not a natural number. 0 is a whole number.

The set of whole numbers is the union of the set of natural numbers and 0.

[–] randint@lemmy.frozeninferno.xyz 9 points 6 months ago* (last edited 6 months ago) (2 children)

Does the set of whole numbers not include negatives now? I swear it used to do

[–] petrol_sniff_king@lemmy.blahaj.zone 8 points 6 months ago* (last edited 6 months ago) (6 children)

That might be integers, but I have no idea.

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[–] Diplomjodler3@lemmy.world 7 points 6 months ago (3 children)

Wait, I thought everything in math is rigorously and unambiguously defined?

[–] NegativeInf@lemmy.world 23 points 6 months ago (1 children)

There's a hole at the bottom of math.

[–] gregorum@lemm.ee 11 points 6 months ago* (last edited 6 months ago)

There’s a frog on the log on the hole on the bottom of math. There’s a frog on the log on the hole on the bottom of math. A frog. A frog. There’s a frog on the log on the hole on the bottom of math.

[–] RandomWalker@lemmy.world 11 points 6 months ago* (last edited 6 months ago)

Rigorously, yes. Unambiguously, no. Plenty of words (like continuity) can mean different things in different contexts. The important thing isn’t the word, it’s that the word has a clear definition within the context of a proof. Obviously you want to be able to communicate ideas clearly and so a convention of symbols and terms have been established over time, but conventions can change over time too.

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[–] TheObviousSolution@lemm.ee 6 points 6 months ago

Zero grew up from the seeds of the undefined, just like negative numbers and people who refuse to accept that the square root only has one value. Undefined is a pathway to many abilities some would consider unnatural.

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