Negative Zero stole my heart
Definition of natural numbers is the same as non-negative numbers, so of course 0 is a natural number.
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.)
But -0 is also 0, so it can’t be natural number.
N0
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.
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.
From what i understand, you can pay iso to standardise anything. So it’s only useful for interoperability.
Can I pay them to make my dick length the ISO standard?
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.
Yeah, interoperability. Like every software implementation of natural numbers that include 0.
How programmers utilize something doesn’t mean it’s the mathematical standard, idk why ISO would be a reference for this at all
Because ISO is the International Organisation for Standardization
Yes, but it’s not for mathematicians. It’s for the applied fields.
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^+.
Yeah dont do that.
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. 😂
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.
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.
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.
It is true.
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.
Of course they’re considered equally viable conventions, it’s just that one is prevalent among Americans and the other isn’t.
I think you’re using a fringe definition of the word “fringe”.
I’m not.
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.
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.
I did say mathematician, not logician.
Logicians are mathematicians. Well, most of them are.
But not all mathematicians are logicians.
Logically.
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 _
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.
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.
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.
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.
0 is natural.
Source - programming languages.
I don’t personally know many programming languages that provide natural number type in their prelude or standard library.
In fact, I can only think of proof assistants, like Lean, Coq, and Agda. Obviously the designer of these languages know a reasonable amount of mathematics to make the correct choice.
(I wouldn’t expect the same from IEEE or W3C, LOL
It’s really just a joke about counting from 0 instead of 1.
Oh, array indexing, sure.
*Most programming languages
We don’t talk about those kids, they’re weird. :)
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.
In school i was taught that ℕ contained 0 and ℕ* was ℕ without 0
I was taught ℕ did not contain 0 and that ℕ₀ is ℕ with 0.
ℕ₀* is ℕ with 0 without 0
Aren’t you guys taught about a tging called whole numbers??
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.
No to both, though atheism can be a theological philosophy.
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.
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.
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?”
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.
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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)
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.
I’m willing to die on this hill with you because I find it hilarious
“I have a number of things and that number is 1”
I have a number of friends and that number is 0
I have a number of money and number is -3567
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.
I think p-adic has that
±ε
Just make star wars universe live action Rick and Morty but crucially WITHOUT Rick and Morty.
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.
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.
Whole numbers are integers, integer literally means whole.
Does the set of whole numbers not include negatives now? I swear it used to do
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.
That might be integers, but I have no idea.
Integer == whole
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.
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
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.
My comment was mostly in jest, it came out all wonky, I shouldnt post sleep deprived :p
This is what we’ve been taught as well. 0 is a whole number, but not a natural number.
How can nothing be a number
Hi, mathematician here. What’s a “number”?
Wouldnt it be best to think of it more as the representation of the absence of something?
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.
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.
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.