• expr@programming.dev
    link
    fedilink
    English
    arrow-up
    92
    ·
    7 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
      link
      fedilink
      English
      arrow-up
      41
      ·
      7 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
        link
        fedilink
        English
        arrow-up
        19
        ·
        edit-2
        7 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
        link
        fedilink
        English
        arrow-up
        12
        ·
        edit-2
        7 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
        link
        fedilink
        English
        arrow-up
        9
        ·
        edit-2
        7 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
        link
        fedilink
        English
        arrow-up
        2
        ·
        7 months ago

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

          • gens@programming.dev
            link
            fedilink
            English
            arrow-up
            6
            ·
            7 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
          link
          fedilink
          English
          arrow-up
          3
          ·
          7 months ago

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

          • WldFyre@lemm.ee
            link
            fedilink
            English
            arrow-up
            1
            ·
            7 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
      link
      fedilink
      English
      arrow-up
      12
      ·
      edit-2
      7 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.

      • xkforce@lemmy.world
        link
        fedilink
        English
        arrow-up
        9
        ·
        7 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.

      • Leate_Wonceslace@lemmy.dbzer0.com
        link
        fedilink
        English
        arrow-up
        7
        ·
        edit-2
        7 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.

      • holomorphic@lemmy.world
        link
        fedilink
        English
        arrow-up
        5
        ·
        7 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 (they/she)@lemmy.ml
        link
        fedilink
        English
        arrow-up
        3
        ·
        7 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
    link
    fedilink
    English
    arrow-up
    74
    ·
    7 months ago

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

  • affiliate@lemmy.world
    link
    fedilink
    English
    arrow-up
    28
    ·
    edit-2
    7 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
      link
      fedilink
      English
      arrow-up
      8
      ·
      7 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
    link
    fedilink
    English
    arrow-up
    27
    ·
    7 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
    link
    fedilink
    English
    arrow-up
    19
    ·
    edit-2
    7 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.

  • Breve@pawb.social
    link
    fedilink
    English
    arrow-up
    13
    ·
    7 months ago

    Other fun arguments in the same vein: Is atheism a religion? Is not playing golf a sport? For extra fun, try explaining the answers to both in a non-contradictory way.

    • doctordevice@lemmy.ca
      link
      fedilink
      English
      arrow-up
      25
      ·
      7 months ago

      How are those the same? You need to define “religion” and “sport” rigorously first.

      Since you haven’t provided one, I’ll just use the first sentence on the wiki page:

      Religion is a range of social-cultural systems, including designated behaviors and practices, morals, beliefs, worldviews, texts, sanctified places, prophecies, ethics, or organizations, that generally relate humanity to supernatural, transcendental, and spiritual elements.

      “Atheism,” without being more specific, is simply the absence of a belief in a deity. It does not prescribe any required behaviors, practices, morals, worldviews, texts, sanctity of places or people, ethics, or organizations. The only tenuous angle is “belief,” but atheism doesn’t require a positive belief in no gods, simply the absence of a belief in any deities. Even if you are talking about strong atheism (“I believe there are no deities”), that belief is by definition not relating humanity to any supernatural, transcendental, or spiritual element. It is no more religious a belief than “avocado tastes bad.” If atheism broadly counts as a religion, then your definition of “religion” may as well be “an opinion about anything” and it loses all meaning.

      If you want to talk about specific organizations such as The Satanic Temple, then those organizations do prescribe ethics, morals, worldviews, behaviors, and have “sanctified” places. Even though they still are specifically not supernatural, enough other boxes are checked that I would agree TST is a religion.

      I have no idea what you’re on about with not golfing being a sport.

        • KISSmyOSFeddit@lemmy.world
          link
          fedilink
          English
          arrow-up
          8
          ·
          7 months ago

          That was not the premise of the poster’s comment.
          0 isn’t nothing, and “a thing” is a much broader category than “natural numbers”.

          Half an apple is also a thing.

      • Breve@pawb.social
        link
        fedilink
        English
        arrow-up
        1
        ·
        7 months ago

        How are those the same? You need to define “religion” and “sport” rigorously first.

        This is really the crux of the argument. There are no absolute authorities on religion, sport, or in the case of the original post, mathematics. We can have definitions by general consensus, but they are rarely universal and thus it’s easy to cherry pick a definition that supports any particular argument with no ability to appeal to authority.

        I have no idea what you’re on about with not golfing being a sport.

        It’s mostly a troll argument, but you can easily trip up people with interchanging the definition of “sport” as a thing (“golf is a sport”) or an activity (“playing golf is a sport”). Then after trying to hammer down the definition more exactly, you can often poke holes in it with more questions like is chess a sport? Is playing Counter Strike a sport? Is competitive crocheting a sport? All of these ambiguities are possible because of the lack of a universal authority in the realm of sports, though some people try to pick an authority such as the Olympics to prove their point.

    • VindictiveJudge@lemmy.world
      link
      fedilink
      English
      arrow-up
      2
      ·
      edit-2
      7 months ago

      I’d argue that atheism is a feature of a belief system and that the system may or may not be a religion. There are religions that don’t feature a belief in any gods. Similarly, your personal belief system may not be a full blown religion, even if you did happen to be theistic.

  • l10lin@lemmy.world
    link
    fedilink
    English
    arrow-up
    11
    ·
    7 months ago

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

    • blind3rdeye@lemm.ee
      link
      fedilink
      English
      arrow-up
      12
      ·
      edit-2
      7 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.)

  • SuperSpruce@lemmy.zip
    link
    fedilink
    English
    arrow-up
    11
    ·
    7 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.

          • petrol_sniff_king
            link
            fedilink
            English
            arrow-up
            1
            ·
            7 months ago

            An English dictionary is not really going to tell you what mathematicians are doing. Like, its goal is to describe what the word “integer” means (in various contexts), it won’t tell you what the “integer series” is.

            https://math.stackexchange.com/questions/138633/what-are-the-whole-numbers

            The gist I see is that it’s kind of ambiguous whether the whole number series includes negatives or not, and in higher math you won’t see the term without a strict definition. It’s much more likely you’d see “non-negative integers” or the like.

            • Monstera@lemmy.ml
              link
              fedilink
              English
              arrow-up
              2
              ·
              7 months ago

              wdym, you know what integers are called in latin languages? “inteiros” (pt), literally “whole”. everyone that does higher math (me included) uses it and understands it for what it is: numbers that are not fractions/irationals.

              Just cause there exists an English hegemony and your language is ill defined and confused with your multiple words for a single concept, that doesn’t mean you get to muddy the waters, rename something in maths, and make a mountain out of a mole hill. Integers include negatives and zero, saying whole numbers and integers is the same, no room for debate

              now excuse me while i go touch some grass

              • petrol_sniff_king
                link
                fedilink
                English
                arrow-up
                1
                ·
                edit-2
                7 months ago

                Whoa, whoa, I’m not making this out to be like an imperialism thing. I’m not interested in what people ought to do.

                The link I gave, a comment in there gives examples of papers where the term is being used to mean different things. So, this ambiguity is either something you just have to contend with (people using the term wrong), or you just don’t read from those people. It’s fine. Nobody is coming for you, I promise.

                If I were in your class and you said “the whole numbers” but meant the negatives too, that’d probably give me pause (dumb American), but I have such herculean powers of intuition that I probably wouldn’t even ask you a question about it.

                • Monstera@lemmy.ml
                  link
                  fedilink
                  English
                  arrow-up
                  1
                  ·
                  7 months ago

                  My comment was mostly in jest, it came out all wonky, I shouldnt post sleep deprived :p

      • anton
        link
        fedilink
        English
        arrow-up
        2
        ·
        7 months ago

        I would say that whole numbers and integers are different names for the same thing.

        In german the integers are literally called ganze Zahlen meaning whole numbers.

  • Codex@lemmy.world
    link
    fedilink
    English
    arrow-up
    11
    ·
    7 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
      link
      fedilink
      English
      arrow-up
      9
      ·
      7 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.

      • reinei@lemmy.world
        link
        fedilink
        English
        arrow-up
        7
        ·
        7 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]).

      • Codex@lemmy.world
        link
        fedilink
        English
        arrow-up
        6
        ·
        7 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.

      • RandomWalker@lemmy.world
        link
        fedilink
        English
        arrow-up
        4
        ·
        edit-2
        7 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.

  • aberrate_junior_beatnik@midwest.social
    link
    fedilink
    English
    arrow-up
    10
    ·
    7 months ago

    As a programmer, I’m ashamed to admit that the correct answer is no. If zero was natural we wouldn’t have needed 10s of thousands of years to invent it.

    • ramble81@lemm.ee
      link
      fedilink
      English
      arrow-up
      10
      ·
      7 months ago

      Did we need to invent it, or did it just take that long to discover it? I mean “nothing” has always been around and there’s a lot we didn’t discover till much more recently that already existed.

      • darthelmet@lemmy.world
        link
        fedilink
        English
        arrow-up
        1
        ·
        7 months ago

        Does “nothing” “exist” independent of caring what there is nothing of or in what span of time and space there is nothing of the thing?

        There’s always been “something” somewhere. Well, at least as far back as we can see.

    • lowleveldata@programming.dev
      link
      fedilink
      English
      arrow-up
      7
      ·
      edit-2
      7 months ago

      As a programmer, I’d ask you to link your selected version of definition of natural number along with your request because I can’t give a fuck to guess

  • AppleMango@lemmy.world
    link
    fedilink
    English
    arrow-up
    9
    ·
    7 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
      link
      fedilink
      English
      arrow-up
      4
      ·
      edit-2
      7 months ago

      Oh no, are we calling non-negative integers “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.

  • NoFood4u@sopuli.xyz
    link
    fedilink
    English
    arrow-up
    9
    ·
    7 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.