[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]

2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

File: 2 KB, 300x168, 다운로드.png [View same] [iqdb] [saucenao] [google]

Anonymous Tue Sep 18 21:26:57 2018 No.10013894 [Reply] [Original]

Is 0 a natural number?

Anonymous Tue Sep 18 21:28:57 2018 No.10013897

>>10013894
it depends on your formulation of the naturals. Peano's original construction used 1 as the lowest element in the naturals; however modern treatments have 0 as the lowest element of the naturals.

it has been shown that it doesn't really matter which one you pick; both are fully consistent and lead to the same math

>>	Anonymous Tue Sep 18 21:29:44 2018 No.10013900 >>10013897 this is objectively wrong shut the fuck up

>>	Anonymous Tue Sep 18 21:30:38 2018 No.10013903 >>10013897 wrong idiot

>>	Anonymous Tue Sep 18 21:30:40 2018 No.10013904 >>10013894 Only if you're a computer scientist

>>	Anonymous Tue Sep 18 21:31:44 2018 No.10013910 >>10013897 Jesus Christ, you're as thick as sticky pigshit. GTFO

>>	Anonymous Tue Sep 18 21:38:44 2018 No.10013925 melvin has arrived

>>	Anonymous Tue Sep 18 21:39:06 2018 No.10013928 File: 552 KB, 2530x1378, why.png [View same] [iqdb] [saucenao] [google] >>10013900 >>10013903 >>10013910 you guys are brainlets, pic related

>>	Anonymous Tue Sep 18 21:41:55 2018 No.10013940 >>10013928 yeah sorry wikipedia is not a proper source around here. kindest regards, melvin

>>	Anonymous Tue Sep 18 21:44:27 2018 No.10013949 based melvin laying down the law

>>	Anonymous Tue Sep 18 21:44:41 2018 No.10013952 >>10013928 >durr i'm right look at this w*kipedia article ummm sorry sweaty,,,,

Anonymous Tue Sep 18 21:47:19 2018 No.10013958
File: 37 KB, 356x499, 51m-9k0V67L._SX354_BO1,204,203,200_.jpg [View same] [iqdb] [saucenao] [google]

>>10013940
well i don't have my undergrad textbook laying around any more, but it used 1 as the lowest member in constructing the naturals

i think it was this one (pic related)

Anonymous Tue Sep 18 21:53:20 2018 No.10013977
File: 186 KB, 998x1400, why2.png [View same] [iqdb] [saucenao] [google]

>>10013958
PS: i even found sundstrom on the web (a newer edition):
https://scholarworks.gvsu.edu/cgi/viewcontent.cgi?article=1007&context=books

and pic related where he uses 1 as the lowest element of the naturals

>>	Anonymous Tue Sep 18 22:00:49 2018 No.10014001 >>10013894 It would be redundant to define N as Z+. There are so many instances where a formula holds for non-negative integers that it becomes a hassle to write Z\Z- and it is easier to just write N.

Anonymous Tue Sep 18 22:12:46 2018 No.10014030

>>10013958
>>10013977
PSS:
thinking about it now, maybe you guys are REEEing over my post for the opposite reasons?

i donno, I learned that 1 is the smallest natural number, but a bunch of undergradfags say "no 0 how i was taught" so i reflexively went to demonstrating that 1 was a legit choice.

however i think most mathfags learn that 0 is the lowest natural nowadays. i leave it to mathfags to post textbook screenshots

>>	Anonymous Tue Sep 18 22:14:19 2018 No.10014034 >>10013940 >>10013952 >this cope t. not the guy you're fiteing with

>>	Anonymous Tue Sep 18 22:35:35 2018 No.10014073 File: 138 KB, 350x350, Naamloos-2.png [View same] [iqdb] [saucenao] [google] Naturally.

>>	Anonymous Tue Sep 18 23:23:18 2018 No.10014173 natural numbers are gay. Z, Z+, Z- Z+0 and Z-0 are the ways to go

>>	Anonymous Tue Sep 18 23:53:12 2018 No.10014240 >>10013894 yes, loads of virgins all over the place

>>	Anonymous Wed Sep 19 00:07:06 2018 No.10014266 [math] \displaystyle \boxed{ \mathbb{O} \; \boxed{ \mathbb{H} \; \boxed{ \mathbb{C} \; \boxed{ \mathbb{R} \; \boxed{ \mathbb{Q} \; \boxed{ \mathbb{Z} \; \boxed{ \mathbb{N}}}}}}}} [/math]

>>	Anonymous Wed Sep 19 01:39:14 2018 No.10014405 File: 7 KB, 686x325, 69864456.png [View same] [iqdb] [saucenao] [google] Weird, 4chan thinks this is spam

Anonymous Wed Sep 19 05:45:33 2018 No.10014672

>>10013900
>>10013903
>>10013910
Fuck off, blatant samefag; it's just a matter of convention.
>>10014030
>maybe you guys are REEEing over my post
Look at the post times of those first three replies, and the number of posts vs. unique posters -- it's just one guy getting triggered.

>>	Anonymous Wed Sep 19 05:49:25 2018 No.10014677 No

>>	Anonymous Wed Sep 19 05:53:43 2018 No.10014686 File: 8 KB, 831x164, Screenshot_2018-09-19 sci - Is 0 a natural number - Science Math - 4chan.png [View same] [iqdb] [saucenao] [google] >>10014672 Mong

>>	Anonymous Wed Sep 19 06:06:38 2018 No.10014699 >>10014686 oh wow so you have several browsers we're real impressed down here

>>	Anonymous Wed Sep 19 06:09:42 2018 No.10014702 >>10014699 fuck off, nerd.

Anonymous Wed Sep 19 06:10:26 2018 No.10014703

>>10013894
some theorems are more beautiful if we start at 0 and some are more beautiful if we start at 1.
for example, if you choose to start at 1, you can define the rationals as having only natural numbers in their denominator, otherwise, you need to specify directly that they can't have 0 in their denominator.
but in CS if you will choose to start from 1 you will have to add a lot of "+1" to a lot of theorems in what seems like a really unnatural manner.

I think it's better to think about the underlying concept of induction rather than the naturals themselves.

>>	Anonymous Wed Sep 19 06:17:36 2018 No.10014713 >>10014405 >skipping \mathbb{N}_0

>>	Anonymous Wed Sep 19 07:51:52 2018 No.10014803 >>10014713 N includes zero, get over it

>>	Anonymous Wed Sep 19 10:44:28 2018 No.10015158 >>10014803 You could use it either way. Make it explicit through the subscript in order to ensure it's interpreted correctly where it matters.

>>	Anonymous Wed Sep 19 10:53:02 2018 No.10015177 >>10014266 based af

>>	Anonymous Wed Sep 19 10:55:34 2018 No.10015184 what's an off-by-one error among friends?

>>	Anonymous Wed Sep 19 10:58:37 2018 No.10015188 >>10015158 >where it matters. it doesn't anon, get over it

>>	Anonymous Wed Sep 19 10:59:07 2018 No.10015189 >>10013894 No

>>	Anonymous Wed Sep 19 11:51:06 2018 No.10015284 >>10013894 0 = 0.000...1 so yes

>>	Anonymous Wed Sep 19 12:59:32 2018 No.10015438 amp-sec

>>	Anonymous Wed Sep 19 13:24:52 2018 No.10015480 >>10013894 Sometimes.

>>	Anonymous Wed Sep 19 13:49:03 2018 No.10015511 Naturals are countable. All counts start at 1. 0 is not natural. One step up, 0 is an integer, along with negative numbers. N = [1, 2, 3, 4, 5, 6, 7, 8, 9, ...] Z = [..., -3, -2, -1, 0, 1, 2, 3, ...]

>>	Anonymous Wed Sep 19 14:23:41 2018 No.10015576 >>10015511 ℕ = {0, 1, 2, …} a+= {1, 2, …} https://en.wikipedia.org/wiki/Natural_number#Notation https://en.wikipedia.org/wiki/Natural_number#cite_note-ISO80000-1

>>	Anonymous Wed Sep 19 14:25:59 2018 No.10015581 >>10015511 N = {0, 1, 2, …} Z+= {1, 2, …} https://en.wikipedia.org/wiki/Natural_number#Notation https://en.wikipedia.org/wiki/Natural_number#cite_note-ISO80000-1

>>	Anonymous Wed Sep 19 14:26:26 2018 No.10015582 File: 10 KB, 686x333, intarray.gif [View same] [iqdb] [saucenao] [google] >>10015511 0 is natural for computers tho fact is you can do either, start naturals at 0 or 1, it's arbitrary

>>	Anonymous Wed Sep 19 14:43:36 2018 No.10015607 >>10013894 shockingly it's a paradox

Advanced search
Text to find
Subject [?]Search by post subject. Leave empty for any.
Username [?]Search for user name. Leave empty for any user name.
Tripcode [?]Search for tripcode. Leave empty for any.
Email [?]Search by email. Leave empty for any.
Filename [?]Search by image filename. Leave empty for any.
From Date [?]Enter what date to start searching from. Format is YYYY-MM-DD
To Date [?]Enter what date to start searching until. Format is YYYY-MM-DD
Image hash
Search in	All Posts OPs Only
Deleted posts	Show all posts Show only deleted posts Only show non-deleted posts
Internal posts	Show all posts Show only internal posts Show only archived posts
Order	New posts first Old posts first
Capcode	All Posts Only by Users Only by Mods Only by Admins Only by Developers
Results	Posts Threads
Action	[ Simple ]