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Zero to hero

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Submitted ⁨⁨1⁩ ⁨year⁩ ago⁩ by ⁨fossilesque@mander.xyz⁩ to ⁨science_memes@mander.xyz⁩

https://mander.xyz/pictrs/image/aea91c9f-934e-454d-aecb-7c3fdf9bea73.jpeg

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  • expr@programming.dev ⁨1⁩ ⁨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.

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    • RandomWalker@lemmy.world ⁨1⁩ ⁨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.

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      • doctordevice@lemmy.ca ⁨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 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^(+).

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      • Emmie@lemm.ee ⁨1⁩ ⁨year⁩ ago

        I hate those guys. I had one prof at uni and he reinvented every possible symbol and everything was so his own. It was a pain in the ass to learn from external material.

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      • Leate_Wonceslace@lemmy.dbzer0.com ⁨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.

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      • gens@programming.dev ⁨1⁩ ⁨year⁩ ago

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

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      • xkforce@lemmy.world ⁨1⁩ ⁨year⁩ ago

        Yeah dont do that.

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    • kogasa@programming.dev ⁨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.

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      • xkforce@lemmy.world ⁨1⁩ ⁨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.

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      • Leate_Wonceslace@lemmy.dbzer0.com ⁨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 conversations 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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      • holomorphic@lemmy.world ⁨1⁩ ⁨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.

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      • pooberbee@lemmy.ml ⁨1⁩ ⁨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.

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  • dogsoahC@lemm.ee ⁨1⁩ ⁨year⁩ ago

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

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    • AnUnusualRelic@lemmy.world ⁨1⁩ ⁨year⁩ ago

      How do you know so much about my life?

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    • aeronmelon@lemmy.world ⁨1⁩ ⁨year⁩ ago

      Image

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    • tate@lemmy.sdf.org ⁨1⁩ ⁨year⁩ ago

      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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      • roguetrick@lemmy.world ⁨1⁩ ⁨year⁩ ago

        There’s a limit to the number of things unless you’re counting spatial positioning as a characteristic of things and there is not a limit to that.

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    • whotookkarl@lemmy.world ⁨1⁩ ⁨year⁩ ago

      How do I have anything if I have nothing of something?

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    • Almrond@lemmy.world ⁨1⁩ ⁨year⁩ ago

      I have seen arguments for zero being countable because of some transitive property with not counting still being an option in an arbitrary set of numbers you have the ability to count too intuitively.

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  • affiliate@lemmy.world ⁨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.

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    • Leate_Wonceslace@lemmy.dbzer0.com ⁨1⁩ ⁨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.

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  • ns1@feddit.uk ⁨1⁩ ⁨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)

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    • Kusimulkku@lemm.ee ⁨1⁩ ⁨year⁩ ago

      “I have a number of things and that number is 1”

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      • assa123@lemmy.dbzer0.com ⁨1⁩ ⁨year⁩ ago

        I have a number of friends and that number is 0

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    • JDubbleu@programming.dev ⁨1⁩ ⁨year⁩ ago

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

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    • porl@lemmy.world ⁨1⁩ ⁨year⁩ ago

      Another Roof has a good video on this. At some points One was considered “just” the unit, and a Number was some multiple of units.

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  • baseless_discourse@mander.xyz ⁨1⁩ ⁨year⁩ ago

    I think if you ask any mathematician (or 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.

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  • RandomVideos@programming.dev ⁨1⁩ ⁨year⁩ ago

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

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    • Faresh@lemmy.ml ⁨1⁩ ⁨year⁩ ago

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

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      • Eylrid@lemmy.world ⁨1⁩ ⁨year⁩ ago

        ℕ₀* is ℕ with 0 without 0

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    • mexicancartel@lemmy.dbzer0.com ⁨1⁩ ⁨year⁩ ago

      Aren’t you guys taught about a tging called whole numbers??

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  • Breve@pawb.social ⁨1⁩ ⁨year⁩ ago
    [deleted]
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    • doctordevice@lemmy.ca ⁨1⁩ ⁨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.

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      • Kolanaki@yiffit.net ⁨1⁩ ⁨year⁩ ago

        To the golf thing:

        “Is not playing a sport also a sport?”

        The basic premise of the poster’s comment was:

        “Is the absence of a thing, a thing in and of itself?”

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    • captainlezbian@lemmy.world ⁨1⁩ ⁨year⁩ ago

      No to both, though atheism can be a theological philosophy.

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    • VindictiveJudge@lemmy.world ⁨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.

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  • pooberbee@lemmy.ml ⁨1⁩ ⁨year⁩ ago

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

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    • jroid8@lemmy.world ⁨1⁩ ⁨year⁩ ago

      no it’s not

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      • darthelmet@lemmy.world ⁨1⁩ ⁨year⁩ ago

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

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      • Sorse@discuss.tchncs.de ⁨1⁩ ⁨year⁩ 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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    • kogasa@programming.dev ⁨1⁩ ⁨year⁩ 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

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    • Collatz_problem@hexbear.net ⁨1⁩ ⁨year⁩ ago

      If we add it as natural number, half of number theory, starting from fundamental theorem of arithmetics, would have to replace “all natural numbers” with “all natural numbers, except zero”.

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      • pooberbee@lemmy.ml ⁨1⁩ ⁨year⁩ ago

        Prime factorization starts at 2, I’m not sure what you mean. Anyway, if you wanted to exclude 0 you could say “positive integers”, it’s not that hard.

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  • l10lin@lemmy.world ⁨1⁩ ⁨year⁩ ago

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

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    • blind3rdeye@lemm.ee ⁨1⁩ ⁨year⁩ ago

      In some countries, zero is neither positive nor negative. But in other, 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 every would even agree that with that definition regardless of whether zero is negative.)

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    • dovahking@lemmy.world ⁨1⁩ ⁨year⁩ ago

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

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  • SuperSpruce@lemmy.zip ⁨1⁩ ⁨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.

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    • randint@lemmy.frozeninferno.xyz ⁨1⁩ ⁨year⁩ ago

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

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      • petrol_sniff_king@lemmy.blahaj.zone ⁨1⁩ ⁨year⁩ ago

        That might be integers, but I have no idea.

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      • anton@lemmy.blahaj.zone ⁨1⁩ ⁨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.

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    • And009@lemmynsfw.com ⁨1⁩ ⁨year⁩ ago

      This is what we’ve been taught as well. 0 is a whole number, but not a natural number.

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    • zaphod@sopuli.xyz ⁨1⁩ ⁨year⁩ ago

      Whole numbers are integers, integer literally means whole.

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  • aberrate_junior_beatnik@midwest.social ⁨1⁩ ⁨year⁩ 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.

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    • ramble81@lemm.ee ⁨1⁩ ⁨year⁩ 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.

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      • aberrate_junior_beatnik@midwest.social ⁨1⁩ ⁨year⁩ ago

        IMO we invented it, because numbers don’t real. But that’s a deeper philosophical question.

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      • darthelmet@lemmy.world ⁨1⁩ ⁨year⁩ 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.

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    • lowleveldata@programming.dev ⁨1⁩ ⁨year⁩ ago

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

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      • aberrate_junior_beatnik@midwest.social ⁨1⁩ ⁨year⁩ ago

        I truly have no idea what you’re saying.

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  • CodexArcanum@lemmy.world ⁨1⁩ ⁨year⁩ 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.

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    • MBM@lemmings.world ⁨1⁩ ⁨year⁩ 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.

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      • reinei@lemmy.world ⁨1⁩ ⁨year⁩ 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]).

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      • CodexArcanum@lemmy.world ⁨1⁩ ⁨year⁩ 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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      • RandomWalker@lemmy.world ⁨1⁩ ⁨year⁩ 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.

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    • Magnetar@feddit.de ⁨1⁩ ⁨year⁩ ago

      But is zero a positive number?

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    • threelonmusketeers@sh.itjust.works ⁨1⁩ ⁨year⁩ ago

      Weird, I learned the exact reverse. The recommended mnemonic was that the whole numbers included zero because zero has a hole in it.

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  • Allero@lemmy.today ⁨1⁩ ⁨year⁩ ago

    Why do we even use natural numbers as a subset?

    There are whole numbers already

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    • NoFood4u@sopuli.xyz ⁨1⁩ ⁨year⁩ 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).

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      • Allero@lemmy.today ⁨1⁩ ⁨year⁩ 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.

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    • zaphod@sopuli.xyz ⁨1⁩ ⁨year⁩ ago
      [deleted]
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      • Knock_Knock_Lemmy_In@lemmy.world ⁨1⁩ ⁨year⁩ ago

        They’re not natural

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  • NoFood4u@sopuli.xyz ⁨1⁩ ⁨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.

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  • AppleMango@lemmy.world ⁨1⁩ ⁨year⁩ ago

    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 ⁨1⁩ ⁨year⁩ ago

    N0

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  • HexesofVexes@lemmy.world ⁨1⁩ ⁨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 ^_^

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  • Toes@ani.social ⁨1⁩ ⁨year⁩ ago

    Negative Zero stole my heart

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  • Diplomjodler3@lemmy.world ⁨1⁩ ⁨year⁩ ago

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

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  • TheObviousSolution@lemm.ee ⁨1⁩ ⁨year⁩ 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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  • pythonoob@programming.dev ⁨1⁩ ⁨year⁩ ago

    Zero is a number. Need I say more?

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  • Mio@feddit.nu ⁨1⁩ ⁨year⁩ ago

    How about minus zero?

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  • moon@lemmy.cafe ⁨1⁩ ⁨year⁩ ago

    How can nothing be a number

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  • bi_tux@lemmy.world ⁨1⁩ ⁨year⁩ ago

    zero is positive

    -dev

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  • werefreeatlast@lemmy.world ⁨1⁩ ⁨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.

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  • Semjaza@lemmynsfw.com ⁨1⁩ ⁨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.

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  • antidote101@lemmy.world ⁨1⁩ ⁨year⁩ ago

    Just make star wars universe live action Rick and Morty but crucially WITHOUT Rick and Morty.

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  • Dkarma@lemmy.world ⁨1⁩ ⁨year⁩ ago

    Science memes…

    Shows a Jedi.

    🤡🤡🤡🤡🤡

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