• expr@programming.dev
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    5 months ago

    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
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      5 months ago

      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
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        5 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
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        5 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
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        5 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. 😂

      • gens@programming.dev
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        5 months ago

        From what i understand, you can pay iso to standardise anything. So it’s only useful for interoperability.

          • gens@programming.dev
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            5 months ago

            I feel they have an image to maintain, but i also feel they would sell out for enough money. So… tell me if you make it.

        • expr@programming.dev
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          5 months ago

          Yeah, interoperability. Like every software implementation of natural numbers that include 0.

          • WldFyre@lemm.ee
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            5 months ago

            How programmers utilize something doesn’t mean it’s the mathematical standard, idk why ISO would be a reference for this at all

    • Kogasa@programming.dev
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      5 months ago

      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
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        5 months ago

        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.

      • xkforce@lemmy.world
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        5 months ago

        The US is one of 3 countries on the planet that still stubbornly primarily uses imperial units. “The US doesn’t do it that way” isn’t a great argument for not adopting a standard.

      • holomorphic@lemmy.world
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        5 months ago

        I have yet to meet a single logician, american or otherwise, who would use the definition without 0.

        That said, it seems to depend on the field. I think I’ve had this discussion with a friend working in analysis.

      • pooberbee (any)@lemmy.ml
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        5 months ago

        This isn’t strictly true. I went to school for math in America, and I don’t think I’ve ever encountered a zero-exclusive definition of the natural numbers.

  • dogsoahC@lemm.ee
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    5 months ago

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

  • affiliate@lemmy.world
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    5 months ago

    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.

    • Leate_Wonceslace@lemmy.dbzer0.com
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      5 months ago

      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
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    5 months ago

    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)

  • baseless_discourse@mander.xyz
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    5 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.

  • Allero@lemmy.today
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    5 months ago

    Why do we even use natural numbers as a subset?

    There are whole numbers already

    • NoFood4u@sopuli.xyz
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      5 months ago

      I’m not too good at math but i think it’s because the set of integers is defined as the set that contains all natural numbers and their opposites, while the set of natural numbers is defined using the successor function - 0 (or 1) is a natural number; if a number n natural, then S(n) is natural where S(n) = n+1.

      • Allero@lemmy.today
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        5 months ago

        Thanks!

        But if we talk whole numbers, we just change the rule that if n is whole, then S(n) is whole where S(n)=n±1.

        Essentially just adding possibility for minus again.

  • Codex@lemmy.world
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    5 months ago

    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
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      5 months ago

      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.

      • Codex@lemmy.world
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        5 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.

      • reinei@lemmy.world
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        5 months ago

        Actually “whole numbers” (at least if translated literally into German) exist outside America! However, they most absolutely (aka are defined to) contain 0. Because in Germany “whole numbers” are all negative, positive and neutral (aka 0) numbers with only an integer part (aka -N u {0} u N [no that extra 0 is not because N doesn’t contain it but just because this definition works regardless of wether you yourself count it as part of N or not]).

      • RandomWalker@lemmy.world
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        5 months ago

        Natural numbers are used commonly in mathematics across the world. Sequences are fundamental to the field of analysis, and a sequence is a function whose domain is the natural numbers.

        You also need to index sets and those indices are usually natural numbers. Whether you index starting at 0 or 1 is pretty inconsistent, and you end up needing to specify whether or not you include 0 when you talk about the natural numbers.

        Edit: I misread and didn’t see you were talking about whole numbers. I’m going to leave the comment anyway because it’s still kind of relevant.

    • Kogasa@programming.dev
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      5 months ago

      There can’t really be an argument either way. It’s just a matter of convention. “Natural” is just a name, it’s not meant to imply that 1 is somehow more fundamental than -1, so arguing that 0 is “natural” is beside the point

  • l10lin@lemmy.world
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    5 months ago

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

    • blind3rdeye@lemm.ee
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      5 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.)

  • AppleMango@lemmy.world
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    5 months ago

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

    • baseless_discourse@mander.xyz
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      5 months ago

      Oh no, are we calling positive integer “whole numbers” now? There are proposals to change bad naming in mathematics, but I hope this is not one of them.

      On the other hand, changing integer to whole number makes perfect sense.

  • SuperSpruce@lemmy.zip
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    5 months ago

    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.