• @l10lin@lemmy.world
    link
    fedilink
    English
    121 year 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
      12
      edit-2
      1 year 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.)

  • @expr@programming.dev
    link
    fedilink
    English
    921 year 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
      421 year 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.

      • @gens@programming.dev
        link
        fedilink
        English
        21 year ago

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

      • @doctordevice@lemmy.ca
        link
        fedilink
        English
        19
        edit-2
        1 year 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^+.

      • @Leate_Wonceslace@lemmy.dbzer0.com
        link
        fedilink
        English
        9
        edit-2
        1 year 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. 😂

      • 𝓔𝓶𝓶𝓲𝓮
        link
        fedilink
        English
        12
        edit-2
        1 year 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.

    • Kogasa
      link
      fedilink
      English
      12
      edit-2
      1 year 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.

      • pooberbee (they/she)
        link
        fedilink
        English
        31 year 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.

      • @Leate_Wonceslace@lemmy.dbzer0.com
        link
        fedilink
        English
        8
        edit-2
        1 year 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
        link
        fedilink
        English
        101 year 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
        link
        fedilink
        English
        51 year 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.

  • HexesofVexes
    link
    fedilink
    English
    51 year ago

    N is the set of “counting numbers”.

    When you count upwards you start from 1, and go up. However, when you count down you usually end on 0. Surely this means 0 satisfies the definition.

    The natural numbers are derived, according to Brouwer, from our intuition of time of time by the way. From this notion, 0 is no strange idea since it marks the moment our intuition first begins _

    • @baseless_discourse@mander.xyz
      link
      fedilink
      English
      1
      edit-2
      1 year ago

      countable infinite set are unique up-to bijection, you can count by rational numbers if you want. I don’t think counting is a good intuition.

      • HexesofVexes
        link
        fedilink
        English
        11 year ago

        On the contrary - to be countabley infinite is generally assumed to mean there exists a 1-1 correspondence with N. Though, I freely admit that another set could be used if you assumed it more primitive.

        • @baseless_discourse@mander.xyz
          link
          fedilink
          English
          2
          edit-2
          1 year ago

          On the contrary - to be countabley infinite is generally assumed to mean there exists a 1-1 correspondence with N.

          Isn’t this what I just said? If I am not mistaken, this is exactly what “unique up-to bijection” means.

          Anyways, I mean either starting from 1 or 0, they can be used to count in the exactly same way.

          • HexesofVexes
            link
            fedilink
            English
            21 year ago

            I’m arguing from the standpoint that we establish the idea of counting using the naturals - it’s countable if it maps to the naturals, thus the link. Apologies for the lack of clarity.

  • @affiliate@lemmy.world
    link
    fedilink
    English
    29
    edit-2
    1 year 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
      81 year 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.

  • @Breve@pawb.social
    link
    fedilink
    English
    131 year 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.

    • VindictiveJudge
      link
      fedilink
      English
      2
      edit-2
      1 year 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.

    • @doctordevice@lemmy.ca
      link
      fedilink
      English
      261 year 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.

  • @ns1@feddit.uk
    link
    fedilink
    English
    281 year 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)

  • @werefreeatlast@lemmy.world
    link
    fedilink
    English
    21 year ago

    So 0 is hard. But you know what? Tell me what none-whole number follows right after or before 0. That’s right, we don’t even have a thing to call that number.

  • @Semjaza@lemmynsfw.com
    link
    fedilink
    English
    11 year ago

    My favourite part is all the replies claiming that their answer to it is correct and it’s not at all controversial.

    Which is funny because to a mathsless individual like me it proves how true the post is.

  • @SuperSpruce@lemmy.zip
    link
    fedilink
    English
    131 year 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.

    • randint
      link
      fedilink
      English
      11
      edit-2
      1 year ago

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

      • @anton@lemmy.blahaj.zone
        link
        fedilink
        English
        21 year 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.

          • @petrol_sniff_king@lemmy.blahaj.zone
            link
            fedilink
            English
            11 year 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
              21 year 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@lemmy.blahaj.zone
                link
                fedilink
                English
                1
                edit-2
                1 year 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
                  11 year ago

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

  • cum
    link
    fedilink
    English
    21 year ago

    How can nothing be a number

    • NoFood4u
      link
      fedilink
      English
      71 year ago

      Because a number isn’t just a representation of a size or amount - that’s called a scalar. A number can also represent a point in a space, the label of a vertex on a graph and probably some other things too.

      • @baseless_discourse@mander.xyz
        link
        fedilink
        English
        2
        edit-2
        1 year ago

        BTW, 0 is typically considered a scalar. As in mathematics scalar is typically defined as a field, which would require an additive identity, namely 0.

  • NoFood4u
    link
    fedilink
    English
    101 year 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.