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/sci/ - Science & Math

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10551476

Anonymous Fri Apr 12 14:27:04 2019 No.10551476 [Reply] [Original]

Can someone explain to me why some people don't think natural numbers include 0?
To me its pretty obvious that natural numbers should include 0.
You can have 1 apple, or 2 apples or no apples.
The same type of logic used for 1 or 2 apples is used for 0 apples.
But as soon as you start talking about negative apples, then this is a different kind of logic, because you have started talking about debts or whatever. So it is rightfully a different set.
What are some of the arguments to not include 0 in the natural numbers?
It's pretty retarded imo.
Another example that comes to me is the speed of a car. It can be 60km/h or 20km/h or stationary(0km/h). These are all "natural" things. But as soon as you are talking about negatives, then this implies moving in some other direction, so this is a completely different kind of discussion. So again it makes sense to include 0 but not negatives.
Why some people exclude 0?
Are they retarded?

>>	Anonymous Fri Apr 12 14:30:03 2019 No.10551492 >>10551476 it's just a name 0 has different properties than the rest so it is reasonable to define a set that excludes it in certain contexts 0 was also more recently defined than the other numbers

>>	Anonymous Fri Apr 12 14:32:13 2019 No.10551497 I thought they did. t. math major

>>	Anonymous Fri Apr 12 14:32:39 2019 No.10551498 >>10551476 For convenience, since dividing by 0 causes problems

>>	Anonymous Fri Apr 12 14:33:43 2019 No.10551503 Naturals are succ(...(succ(0)).

>>	Anonymous Fri Apr 12 14:35:25 2019 No.10551507 >>10551476 X apples = X bananas Only works for X = 0, which makes it special.

>>	Anonymous Fri Apr 12 14:36:53 2019 No.10551512 Peano’s axioms actually includes it as the seed to natural numbers by which all other natural numbers can be included with the succesor definition or something Oh and I’m probably a faggot

>>	Anonymous Fri Apr 12 14:37:13 2019 No.10551514 All right look at it this way. When a babby is counting something they always start with 1. So in some ways it is more natural to start with 1.

>>

Anonymous Fri Apr 12 14:39:53 2019 No.10551525

>>10551492
I'm not arguing that there shouldn't exist different sets.
I'm talking about the name natural.
It may be just a name but names are important.
0 is a natural thing that occurs in nature. It is the absence of something.
Negatives are unnatural since they are just abstractions we use to explain things.
There are people who use the name natural to describe positive integers and I find this very annoying.

>>

Anonymous Fri Apr 12 14:40:05 2019 No.10551527

It's completely arbitrary whether or not to include them. I've heard that in Europe it typically includes 0 and in America it typically doesn't, but that's not a strict convention or anything it's just what's common. Remember, math is a means of communicating quantifiable information, there isn't an objective way to declare what the natural numbers include. I prefer defining natural numbers to be the set of possible cardinalities for finite sets, which of course includes 0. Then, if I want to be clear that 0 shouldn't be included in my set, I can simply say "positive integers" which is unambiguous. But that's just a personal preference, I am not opposed to 0 not being included as long as the paper makes it clear.

>>	Anonymous Fri Apr 12 14:45:42 2019 No.10551539 >>10551527 This, I think most math guys say positive integers (or nonnegative integers to include zero).

>>	Anonymous Fri Apr 12 14:48:24 2019 No.10551552 >>10551525 If you're going to talk about things that have bad names, you're tilting at windmills. names USUALLY don't tell the whole story

>>

Count von Count Sat Apr 13 04:18:57 2019 No.10553549
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1) the phrase "natural numbers" is a misnomer. There is no number in nature. Numbers are an idea constructed by people.
2) the first set of numbers were counting numbers. If there is no item to count, then counting cannot be done, therefore zero is not a counting number.
3) none of this is a difficult concept.

>>	Anonymous Sat Apr 13 04:43:11 2019 No.10553579 >>10551476 It's an inconsistent term some people consider the set "natural numbers" as including zero, and others do not. It's a reason why people just say non-negative integers or positive integers instead.

>>

Anonymous Sat Apr 13 04:46:18 2019 No.10553585

>To me its pretty obvious that natural numbers should include 0.

>You can have 1 apple, or 2 apples or no apples.

I don't give a fuck how you define the natural number, the countable ordinals or whatever, but the way you frame it exactly gives the justification for why one would not include them. You emphasis in your language how there's a conceptual difference between 0 and the others.

>>	Anonymous Sat Apr 13 08:28:02 2019 No.10553898 >>10551527 Right now I have 0 black holes, 0 pants, 0 tables, 0 tablets, 0 flowers,... in my hand. That doesn't feel natural.

>>	Anonymous Sat Apr 13 08:36:25 2019 No.10553927 There's nothing natural about zero

>>	Anonymous Sat Apr 13 17:28:08 2019 No.10555296 >>10551527 >I've heard that in Europe it typically includes 0 Where the fuck did you get this. Math is equal in on all sides of the earth. stupid amerilard.

>>	Anonymous Sat Apr 13 17:31:34 2019 No.10555309 >>10551476 Because literally every other element can be written as 1+1+1+...+1, and because it bloats the axioms. >>10551512 Peano's original axioms didn't have zero.