Is 0 a natural number?

[Anonymous No.15676299]

Among the many topics in mathematics that cause controversy between the community, one of many is the question whether 0 is a natural number or not. In my undergrad algebra classes, it was always a topic to comment on. Specially when we were learning about Logic and the ZF or Peano axioms.

Historically, the number zero appears much later than any other natural number. Some civilizations like the Romans used numeration systems that lacked the 0, for example. It makes much more sense that it appeared along the integers whenever you subtracted a number with itself (or you added a number with its opposite). Yet still a lot of mathematicians accept the number zero as a natural. Proofs and axioms are being written with this information, sometimes because they can be much easier this way.

What does /sci/ think about it? Is it a natural number? Or should it be considered an integer?

[Anonymous No.15676305]

>>15676299
Can you have 0 things? No? Then it's not a natural number. Why does it matter? Why do you want it to be a natural number?

[Anonymous No.15676312]

>>15676299
No. But it's a whole number. (I learned this in pre-K.)

[Anonymous No.15676322]

Natural numbers should start at 1 in my opinion.
Then operations like exponentiation, division, and roots give definitive results for all natural numbers.
Otherwise you have things like [math]0^{0},\frac{0}{0},\sqrt[0]{n}[/math]
Since 0 is more like the absence of a number after all.

[Anonymous No.15676337]

>>15676299
>In my undergrad algebra classes, it was always a topic to comment on.
Obviously you'll always clarify notation, it's not really "controversial".
That said it's kind of a waste to not include 0 when 'positive integers'/Z^+ is already a thing. Maybe excluding 0 would be more convenient for induction but lots of cases would also exclude 1 either way.

[Anonymous No.15676353]

>>15676299
Having 0 as a natural number is essential to make algorithms that work on natural numbers work in an easy way that a second grade child could understand or some engineer faggot could implement in silicon. So 0 is a honorary natural number simple as.
>>15676305
Yes you can have 0 apples. Having 0 apples is more natural than 1.23 apples or 1+√2 apples

[Anonymous No.15676355]

>>15676305
Pretty sure most people here have 0 girlfriends

[Anonymous No.15676357]

>>15676353
In the same way that an honorary degree is a degree.

[Anonymous No.15676371]

>>15676353
>you can have 0 apples
Golems literally cannot tell the difference between abstractions and reality.

[Anonymous No.15676381]

>>15676353
0 apples = not having an apple
for every natural number like 1, 2, 1243564565, you have an apple.

[Anonymous No.15676426]

>>15676371
>casual antisemitic rhetoric
it's so tiresome. You're better than this.

[Anonymous No.15676430]

>>15676299
This is a non-issue.

[Anonymous No.15676476]

>>15676426
I live in Israel and know that antisemitism is fully deserved. Especially towards American Jews. If your let gets literally holocausted, I will applaud.

[Anonymous No.15676491]

>>15676476
>t. 4channel ambassador from the imaginary nation of "Palestine"

[Anonymous No.15676494]

>>15676491
I'm not a shitskin. Palestine is as much an artificial fabrication as Israel.

[Anonymous No.15676549]

>>15676312
I thought you meant 'integers' but apparently there's a different set for all naturals plus the zero. In Spanish we translate 'whole' and 'integer' as 'entero', so maybe the concepts are mixed in here.

>>15676322
Not a bad reasoning, but the root of degree 1 is not a thing either. Sure it can be done, but who really uses it?

[Anonymous No.15676668]

>>15676549
American children learn blackboard font W to include 0 before age 2. I'm sorry that another country's education is subpar but I can't help—you guys just need to vote better.

[Anonymous No.15676849]

arguing that 0 isn't natural because you have to exclude it for your induction proofs to work properly is as retarded as saying that 2 isn't prime because of how many proofs require treating it as a separate case from the others

[Anonymous No.15676888]

>>15676849
Arguing that 2 is prime because it's special is nonsense. 2 is prime because no integer other than 2 or 1 can divide 2.

[Anonymous No.15676958]

>>15676299
doesn't matter
just make sure the person you're communicating with knows whether or not you're including 0

[Anonymous No.15677075]

>>15676888
didn't say that it was prime because it was special
but if I had a nickel for every proof I had been made to do that said "this is true of all primes. here's how we treat 2, and here's how we treat every odd prime"...

[Anonymous No.15677087]

>>15677075
2 is a special prime because it's even but it's not special because it's even.

[Anonymous No.15677142]

>>15676299
context-dependent yes and no

[Anonymous No.15677210]

>>15677142
That's a lame way to avoid the question. 0 is never part of N unless you specifically define N to inculde 0.

[Anonymous No.15677252]

>>15677210
0 is part of N in europe, you burger

[Anonymous No.15677265]

>>15676299
Not natural, however for practical purposes is convenient to put it with them.

[Anonymous No.15677271]

>>15677265
is that boat, a shark or a paper plane that the middle guy is holding?

[Anonymous No.15677281]

>>15677252
No it's not. You collectivist shit.

[Anonymous No.15678678]

>>15677271
>is that boat, a shark or a paper plane that the middle guy is holding?
Scientifically speaking, you seem to have a keen eye. Could you tell me what this is? Is it computer-drawn or a photograph? Of what?

>>15676849
The idea that 2 is not a prime number is a fascinating idea, thank you. Have a youtube video: https://www.youtube.com/watch?v=B1J6Ou4q8vE&t=155s

[Anonymous No.15678864]

>>15677281
Source? I also live in Europe and I disagree. In what country do you live?

>>15676299
It makes perfect sense for 0 to be inside the set of natural numbers.

Yes, you can have 0 apples (or 0 girlfriends, lol).

[Anonymous No.15678886]

>Peano's arithmetic explicitly defines 0 to be a natural number
>canonical construction of natural numbers in ZF set theory explicitly defines 0 to be a natural number
>type theory explicitly defines 0 to be a natural number
There's no debate outside undergrad loser study groups really.

[Anonymous No.15679019]

>>15678678
well i know its an AI filter over the kanye infowars appearance, but id say it looks like a boat with some circles on the form that could be considered to allude at a shark decal

[Anonymous No.15679187]

>arguing over definitions

[Anonymous No.15680339]

>>15676299
Historically
no

Aristotle and Jesus did not use zero

SIRS
BOW AND SAY NAMASTE PLEASE

[Anonymous No.15680366]

>>15680339
>he does not know of the greeks use of babilonian numbers(which had a zero) inspired system on-top of their numerals for astronomy
kek
https://en.wikipedia.org/wiki/Greek_numerals#Zero