Is 0 a natural number?

Should you define it to be

no, if it was natural it wouldn't have taken hundreds of years longer to come into use after the other naturals

yeah why not

50/50 chances of it being one, either it is or is not.

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yes

>>9020707
The housing market will never founder, real property's value always outweighs its risk. Axioms are always true... until they're not.

>>9020728
Those aren't axioms they are assumptions. I seriously hope economy retards don't call their stupid models axioms.

>>9020733
So what about an `infinite set'? Well, to begin with, you should say precisely what the term means. Okay, if you don't, at least someone should. Putting an adjective in front of a noun does not in itself make a mathematical concept. Cantor declared that an `infinite set' is a set which is not finite. Surely that is unsatisfactory, as Cantor no doubt suspected himself. It's like declaring that an `all-seeing Leprechaun' is a Leprechaun which can see everything. Or an `unstoppable mouse' is a mouse which cannot be stopped. These grammatical constructions do not create concepts, except perhaps in a literary or poetic sense. It is not clear that there are any sets that are not finite, just as it is not clear that there are any Leprechauns which can see everything, or that there are mice that cannot be stopped. Certainly in science there is no reason to suppose that `infinite sets' exist. Are there an infinite number of quarks or electrons in the universe? If physicists had to hazard a guess, I am confident the majority would say: No. But even if there were an infinite number of electrons, it is unreasonable to suppose that you can get an infinite number of them all together as a single `data object'.

>>9020745
wildberger is the living meme of math

>>9020674
Hey anon, I know you're always shitposting on this and dunno if I can get a reasonable answer but.

Does this series prove the universal 50/50?
>https://en.wikipedia.org/wiki/Grandi%27s_series

>>9020644
We really need to start using different terms to refer to "the naturals with zero" and "the naturals without zero".

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>>9020644
Nice bait

no, it is an artificial number produced in nuclear reactors and supernovae

of course it's a natural number. the set N includes by definition. it's a whole number greater than or equal to zero. N+ doesn't have zero if that's what you wanna use, but if you fuck with my sets, i'll beat you like a runaway slave.

>>9020644
According to the ISO standard, yes. If you're one partial to preferring a coherent standard, like me, then you'll just go with it, at least for now.

In terms of Mathematical logic, I would say yes it is.
In plain terms, does it really exist in nature, in a physical sense? The obvious answer is no, especially when considering this >>9020646
However, maybe you can consider it the absence of a number or value, not the 0 that we think of in a number system, not as a number but more raw. While it doesn't exist as a physical item, it does exist in it being a lack of physical items. Numbers weren't defined so clearly, especially not without some fleshed-out base system, far in the past. We shouldn't look through the lens of base 10 and modern Mathematics if we want to define it this way. So it depends if you consider absence of value, to be something fairly naturally known and practically applied.

...is any number a "natural" number?
No.
Step outside mom's basement, and look for
a number. You will find none, Spanky.
They are all ideas, in our minds.

"natural number"
If mathematicians would go outside, they would
discover that numbers (of any kind) are not
"natural"... but they don't.

>>9020646
just because some brainlet caveman decided to not include 0 doesnt mean which should stick to their brainlet ways forever

Sometimes it's more convenient to include 0, sometimes it isn't, I just wish we had consistent standards on how to denote either instead of [math]\mathbb{N}_0, \mathbb{Z}^+[/math] and having to guess which is meant when you see just [math]\mathbb{N}[/math].

>>9020644
>Is 0 a natural number?

Zero is the absence of number.

>>9020644

It is, except when it's not.

>>9021101
Demand labeling laws for math textbooks. Numbers are unnatural and the consumer has a right to know.

>>9020644

Several prominent authors, depending on their purposes, either do or do not include zero. There are times when it makes sense to include zero in your discours, and there are times when it makes sense to exclude it. But two things are perfectly clear, just from a conventional, notational perspective:

1) We have well-understood notations for things like integrals, matrices, polytopes, richer number systems, and so on. In view of this, it is absolutely idiotic that there should be any further mental energy spent on "whether zero is a natural number, or not", since the substance of the question is only a notational one.

2) In view of 1), the mathematical community should obviously, and once and for all, get together and agree on names for each of the following two sets:

[eqn] S_1 = \{1,2,3,...\} [/eqn]

[eqn] S_2 = \{0,1,2,3,...\} [/eqn]

Notice above all /that it does not matter which set ends up getting called what/. What matters is that a consensus and a consistent notation be agreed upon going forward, and that /two different names be used/. This, exactly because situations regularly arise where one wishes to employ S_1 to the exclusion of S_2, and vice verse (in the sense that one must always account for the possibility of zero, in the latter case).

>>9021566
I agree, except when I don't.

>>9020644
No.