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.
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.
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.
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.
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.
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.)
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.
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.
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 ^_^
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.
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.
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.
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.
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.
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.
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.
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.
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