Mathematicians can't even agree on whether zero is a natural number

>mathematicians can't even agree on whether zero is a natural number
This is why no one takes you seriously, mathfags.

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If us superphyiscists managed math, it would be a lot better.

This issue sounds ridiculous. Just put in some definition N\{0} and fuck off.

>math

Zero is not a natural number. There is no confusion

No it isn't. Natural numbers are 1, 2, 3, ... while whole numbers are 0, 1, 2, 3, ....

mathworld.wolfram.com/NaturalNumber.html
>The term "natural number" refers either to a member of the set of positive integers 1, 2, 3, ... (OEIS A000027) or to the set of nonnegative integers 0, 1, 2, 3, ... (OEIS A001477; e.g., Bourbaki 1968, Halmos 1974). Regrettably, there seems to be no general agreement about whether to include 0 in the set of natural numbers.

I mean does it really matter? You can construct the naturals with zero or not doesn't make a difference

>directing to /x/

I have never seen 0 included in the natural number set

>Speakers of the English language can't agree on how to spell colour

I've always seem zero in the natural numbers set.
How do you even define natural numbers without zero in ZFC ?

"natural" (L0L as if) numbers are congruent
to "counting" numbers, which do not include
zero ~ if there are zero objects, then there is
no counting. This is not a difficult concept.

a priori, you can't know there are zero objects of some kind until you attempt to count them. Since there might not be any such objects, you might count 0 of them. This is trivial to understand.

start with 1 instead?

CS and type theory also seems to agree.

data ℕ : Set where
Z : ℕ
S : ℕ → ℕ

Math threads belong to

Except it is. Natural numbers are finite cardinalities, which means they include zero.

You literally take the least inductive set, and then take zero out. It's pretty stupid.

>mathematicians can't even agree on whether zero is a natural number
That's because in some fields or some particular problems zero is needed and in others not. Instead of saying "natural" and "natural including zero", or "natural" and "natural without zero" in every fucking sentence you just claim your naturals once to be what you need it to be and use it.

The idea of naturals is redundant and retarded even without this ambiguity. Why don't we just use "integers", "positive/negative integers" and "non-positive/non-negative integers" instead?

>The idea of naturals is redundant and retarded even without this ambiguity. Why don't we just use "integers", "positive/negative integers" and "non-positive/non-negative integers" instead?
>I have no idea how to build naturals and integers: the post

Naturals are just either positive or non-negative integers, depending on whether you include zero, aren't they?

forced memes belong in and

Nah you build integers off naturals, not the other way around.

>I still have no idea how to build naturals and integers: the post

Why even botter about this? Mathfags are such a freaks!

dude why bother with integers lmao
just define them as "rounded real numbers"
in fact why bother with reals, just define them as the real part of complex numbers roflXD

Equivalence classes? I had algebra years ago, I don't remember shit.
Whatever you build your shit, positive integers are still equal to naturals respectively. And negative integers are just inversed positive integers.

There's an obvious bijection between positive integers and natural, but no they are not the same thing.

What's the difference between a natural 1 and an integer 1?

Sure, and integers are just rationals that have the denominator equal to one. And rationals "are just" reals that aren't irrational. Doesn't change the fact that it's generally customary to consider simpler ideas before the more complex ones.

Integer 1 is the equivalence class of the ordered pair (1,0) (where 1 and 0 are naturals)

>but no they are not the same thing.
Most texts take them as the same thing.
I can't count how many books have the typical
[eqn] \mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C} \subset \mathbb{H} [/eqn]

You say you took algebra years ago, yet you somehow missed real analysis (or your real analysis class somehow skipped constructing the reals).

nothing

So, zero is natural now?

Dude, numbers are just there. Only mathfags care about this shit.

Well yeah, if you want your naturals to be a group.

Yeah, it really is a shorthand though.

*(2,1)
:^)

>or your real analysis class somehow skipped constructing the reals
We used Dedekind's cut. I don't remember seeing any "natural numbers" in it and especially distinguishing between "naturals" and "integers".

So, zero is not natural now?

The integer 1 has an additive inverse. The natural number 1 does not.

>We used Dedekind's cut

>if you want your naturals to be a monoid

ftfy

woops

> implying massive mathfag faggotry

>Dude, numbers are just there. Only mathfags care about this shit.
>Dude, particles are just there. Only physicsfags care about this shit.
>Dude, chemicals are just there. Only chemfags care about this shit.
>Dude, cells are just there. Only biofags care about this shit.

Dude, shitposts are just there. Only faggots care about this shit.

Dedekind cuts are sets of rationals, which are constructed from integers, which are constructed from _________.
I'll let you fill in the blank.

Inverses are pretty important user. This is mathfaggotry 101.

...

Thank you user. You're a based mathfag.

Uhmm, memes involving moe animu girls? Amirite?
Tell me user, I'm curious. :з

Potato?

>you can't know there are zero objects of
>some kind until you attempt to count them
wat

0 is a finite cardinal.
0 is a finite ordinal.
0 is a natural number.
End of debate, US brainlets.

*color

0 is the neutral element. Therefore it can be part of natural numbers.

We don't always need it though.

/thread

>Doesn't change the fact that it's generally customary to consider simpler ideas before the more complex ones.
Really there's no good justification for this.

0 is also infinite.

So how do you define integers if you don't defiine naturals first? Legit curious.

1. define positive integers the way you define natural numbers usually
2. add a - sign for negative
3?
4) profit

naturals are simpler and should be defined first

its free to pick you idiot.

>I define integers without naturals by defining naturals and just calling them positive integers

Let's create a term and fight over if something is or not part of that term.

Seriously?

additive identity is srs bzns

you must be new here

>Math doesn't belong in Science and MATH forum

Meh, that's boring and lacks all of the mathematical elegance numbers actually possess.

It really just depends on the application, doesn't it?
In all my Computer Science lectures, the natural numbers include 0, but in my calculus and linear algebra classes, the natural numbers started at 1.
I imagine other subjects like Physics, Geology, Biology etc use definitions that fit them

More importantly it's fucking retarded and wrong.

>but in my calculus and linear algebra classes, the natural numbers started at 1.
Who the fuck does that? Who the fuck defines the naturals without a neutral element? For what purpose?

why is foundations math always so fuckin boring and gay it's all useless memes shit and is not even "beautiful" like number theory which is at least autism with a little fucking flavor; sperm jacked off onto prime numbers and swallowed by cockfags with little imagination.

>neutral element
The natural numbers cannot form an algebraic group, anyway, due to the lack of an inverse element. So who cares if a neutral element exists?

see

Funnier thing is people think there are numbers greater than 10^200

Huge butthurt detected

what

Of course there are numbers greater than 10^200. 10^199, for instance.

You've never seen a construction of the naturals in set theory (protip: empty set = 0)?

Idiots.

The highest number is 9.

It's less from both 10^200 and 10^199.

Those numbers are less. Every tenth is just a new construction, therefore 9 is the highest number.

Get wrecked, pleb.

zero contains all numbers i learned this on numberphile

therefore it is a natural number and a real number and an irrational number, also an odd and prime

literally 10^201 is higher idiot

that just means that you're such an undergrad kid that you've only ever used one or two textbooks or only had one or two lecturers.

when you aren't such a little kiddy and have done more math you'll see that whether 0 is in the natural numbers depends from source to source

A lot of proofs look nicer if 0 is excluded

graham's number is bigger though

I'm dying

In France, we consider :
0 is a natural number
a is greater than b a >= b
a if lesser than b a = 0
a is negative a

>In America
stopped reading there

...

Not in base 206 or higher.

>as though any number is "natural"
fgt pls

this is way more logical

such as?

>directing to /trash/

>Implying reals exist

0 can't be natural in Catholic country, I bet u live in some Western islamist jihadist state

Natural numbers are defined as strokes on board. You can't draw zero strokes so zero is not a natural number