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/sci/ - Science & Math

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5309894 No.5309894 [Reply] [Original]

Define zero. Go.

>> No.5309895

your phallic diameter

>> No.5309896

your IQ

>> No.5309898

Additive neutral element.

>> No.5309901

>>5309895

Can you measure zero?

>> No.5309902

Your chance of ever getting laid.

>> No.5309906

it's qualia, and so indefinable, you nincompoop

>> No.5309909

"sthānāt sthānaṁ daśaguņaṁ syāt which means "from place to place each is ten times the preceding" - Aryabhata

I'll go with that.

>> No.5309910

the number of fucks I give

>> No.5309911

>>5309901
no, the phallic wave function collapsed when the female caused the observer effect

>> No.5309912

>>5309910
its also your post number.

>> No.5309915
File: 1.25 MB, 2560x1920, Mandel_zoom_00_mandelbrot_set.jpg [View same] [iqdb] [saucenao] [google]
5309915

Everything.

>> No.5309917

>>5309911
Women can't collapse the wave function. Only conscious observers can collapse it. Females are p-zombies.

>> No.5309923

>>5309910
've* n*

>> No.5309927

>>5309917
touché

>> No.5309933

India invented it to express the value of their civilization.

>> No.5309936

santa claus

>> No.5309978

-3, -2, -1, 0, 1, 2, 3,

>> No.5309996

Cardinality of the empty set.

>> No.5309997

The sum of all numbers.

>> No.5309998

the empty set itself.

>> No.5310000

an empty whisky glass in a bright winter morning

qualia

>> No.5310006

0 is the neutral element regarding +

>> No.5310007

Given a the set Z where Z is the integers.
We form a commutative ring with the binary operators + and *
0 is the identity for the operator +

>> No.5310008

The thing for which the Successor function yields 1.
(1 being the thing for which the Successor function yields 2.
(2 being the thing for which the Successor function yields 3.
....
)))...)))

>> No.5310010

0 is a number such that a + 0 = a and a*0 = 0.

>> No.5310017

0 is an imaginary number. It does not exist in the real world.

>> No.5310019

>>5310007
> has the integers
> already has zero
protip: zero is the pair of equal naturals

>> No.5310022

For a given ring (R,+,*), there exists an element 0 in R that satisfies the axiom x+0=x.

>> No.5310034

It's one less than one.

>> No.5310035

the number of gods in this universe

>> No.5310038

>>5310022
But... then only rings have 0. What about naturals and integers?

>> No.5310039

>>5310022
> for a given ring
if the ring is given, zero is given. Try again.

>> No.5310040

>>5310038
>integers
>not a ring

ya blew it

>> No.5310041

>>5310039
Then, what he said was not false.

>> No.5310042

>>5309996
i like this answer the most so far

>> No.5310044

>>5310040
Gah. I was thinking about fields. I stand corrected.

>> No.5310046

>>5310041
To prove it is a ring, you have to already have defined zero. So, you see, it doesn't work to "define zero." The idea of zero is prior to rings. Ya dig?

>> No.5310059

>>5310038
>Z not a ring
u wot m8?

also N forms a semiring (if you define N to include 0 as an element).

>> No.5310069

>>5310035
>in this universe
No dip, Sherlock. Nobody believes that there's a god in this universe.

>> No.5310070

>>5310046
You need an element that acts as a zero, but you still need to figure out which element it is.

What about defining it as the cardinality of the empty set?

>> No.5310077

>>5310070
How about a group? Groups have zeros, and rings are groups. What's algebraically prior to groups?

>> No.5310086

>>5309997
>implying negative numbers exist in natural world

>> No.5310088

>>5310077
generally multiplicative notation is used for groups... if we use additive notation, it's generally assumed the group is abellian. So, the neutral element in an abellian group?

>> No.5310093

>>5310077
Monoids, then magmas.

>> No.5310098

>>5310088
I'd prefer the neutral element in an abelian monoid. That way we cover the naturals with zero.

>> No.5310111

>>5310093
Magmas don't have to have an identity element for its operator though. So I'd guess monoid is the base case as far as algebraic structures go.

>>5310070
I'm not intimately familiar with the development of set theory. It's my understanding, but I might be wrong, that the entire notion of cardinality requires a prior definition of numbers including zero. I say this because I don't think the cardinal numbers are identical with counting numbers (due to alephs).

>> No.5310124

>>5310111
At one point in time cardinalities were identical with counting numbers. As far as I know, they still are, except for the case of transfinite sets

>> No.5310127

>mfw all these first year math undergrads who are way too proud of knowing their babby's first algebraic structures

too much pseudo-intellectualism ITT

>> No.5310131

>>5310124
If so it seems the cardinality of the empty set is indeed the best definition available.

>> No.5310138

Number 0 for which the following property holds for all x:

x + 0 = x

>> No.5310161

a + b = a

b is defined as zero for all a.

>> No.5310167

the number of gf's that OP has had

>> No.5310178

In ZFC, the ordinal numbers (of which the naturals are a subset) are generally taken to be sets containing all the prior ordinals.

So for example
0 = {}
1 = {0}
2 = {0, 1}
3 = {0, 1, 2}
<span class="math">\omega[/spoiler] = {0, 1, 2, ...}
<span class="math">\omega[/spoiler] + 1 = {0, 1, 2, ..., <span class="math">\omega[/spoiler]}

>>5309996 and >>5309998 are both in agreement with the usual definitions because the cardinality of a set is taken to mean the smallest ordinal with that cardinality.

Of course, this is in reference to the natural number zero. The integer zero, the rational number zero, the real number zero, and the complex number zero are all different objects in this way of thinking.

>> No.5310195

>>5310127
u jelly

>> No.5310197

>>5310195
Jelly of what? Of your freshman arrogance? lol no

>> No.5310206

Of course untyped set theory isn't the only game in town.

One option is to axiomatize the naturals directly instead of expressing them in terms of sets, and in that case, zero and the successor function are primitive objects with no definition.

Here's the Church encoding of zero:
<span class="math">\lambda f.~ \lambda x.~ x[/spoiler]
Or in the Calculus of Constructions, where we need to give our variables types:
<span class="math">\lambda A : {\rm Prop}.~ \lambda f : (A \to A).~ \lambda x : A.~ x[/spoiler]

In Coq, the naturals are introduced with its inductive type mechanism:
Inductive nat : Set := O : nat | S : nat -> nat.

>> No.5310210

>>5310197
^ he jelly

>> No.5310218

>>5310019
*set of pairs of equal naturals

>> No.5310243

0 = harbl = everything, but nothing at the same time.

>> No.5310534

OP here. I enjoyed your discussion /sci/.

pic is of sir Andrew Wiles...OP confirmed.

>> No.5310536
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5310536

>>5309896
lel

>> No.5310539

You had three apples!
I took three of them!
How many apples do you have now!?

>> No.5310547

The midpoint of the relationship formed by any thing and that thing's direct opposite.

>> No.5311522
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5311522

>>5310069
Fuck off I believe there's a God ... period.


inb4 dumbfuck

/NO U

>> No.5311553

>>5311522

Oh fucking boy here we go.

erryones gonna get autobanned for rule #3

>> No.5311556

>>5310178
I think any theory where the naturals is not subset of integers not subset of rationals not subset of reals not subset of complex is crap.

>> No.5311559

>>5310017
Does anyone seriously consider some numbers to exist while others do not? That's so... plebeian highschool qualia.

I mean does anyone concerned with the philosophy of mathematics believe this?

>> No.5311561

>>5309894
The absence of value.

>> No.5311568

Identity of additive group
(multiplicative) linear map on some space whose kernal is the space itself

>> No.5311573
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5311573

>>5311559
>plebeian highschool qualia.

>> No.5311587

Define 1 is a lot harder.

>> No.5311608
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5311608

>>5311587
A measurement in quantity, in which the value one is associated with a singular entity.
For example, this is a drawing of 1 cow.
>/sci/ in charge of over complicating things.

>> No.5311610

>>5309894
Zero has no actual meaning. Unless you define context it's just a symbol.

>> No.5311615

>>5311587
Successor of zero, or {{}}.

>> No.5311641

It is not an object onto itself, but rather a concept that arises from relations between other ideas.

I think it is pointless to try and find a definition of what a particular number like zero should be. It is more fruitful to define the notion of number, and to illustrate this definition by that of zero.

>> No.5311658

>>5311608
define "singular"

>> No.5311703

>>5311658
define "define"

>> No.5311710

>>5309997

This.

>> No.5311720

n minus n

>> No.5311721

>>5309917
Had to giggle.

8/10

>> No.5311722

>>5311720
wait shit

>> No.5312871

A zero? Uhh..
Like a zombie with acne and a pale face with no jawline and bad teeth with a flat chest and uneven muscel tone with bad fashion sense and no job

>> No.5312906
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5312906

>>5311720

>> No.5312913

>>5311720
Tell that to wheel theory. Come on; use your fucking brain people.

>> No.5312911
File: 650 KB, 800x879, Zero01.png [View same] [iqdb] [saucenao] [google]
5312911

>>5309894

>> No.5312914

>>5309917
I love you. I think you're making me turn gay: after reading your comments, I almost wanted to suck your cock and study engineering.

>> No.5312916

>>5312911
it's like they tried to make this character appeal to 14 year olds in every way possible, including his name. "zer0" are you fucking kidding me

>> No.5312928

>>5312916
I have to agree with you there, but you gotta admit it's a pretty cool character. Plus those comments you get when you make head shots etc lol

>> No.5312934

>>5312928
>but you gotta admit it's a pretty cool character
nope

>> No.5312942

>>5312916
>they tried to make this character appeal to 14 year olds
>you gotta admit it's a pretty cool character
QED, faggot.

>> No.5312944

n-n where n is any number.

>> No.5312953

>>5312944
see
>>5312913

In wheel algebra, x-x does not always equal 0.

>> No.5312958

>>5312942
Fuck you, I'm 21. To each his own; I think it's tight.

>> No.5312968
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5312968

>>5312958
>I think it's tight.
>tight
confirmed for 14

>> No.5312988

>>5311703
define "define "define""

>> No.5313025

0 = the sum of 1 and -1

>> No.5313036

0 = 1 + (-1)

1 represents creation
-1 represents destruction

>> No.5313041

>>5313025
>>5313036

Real numbers don't take into consideration other variables that could also lead to a zero answer. It should be:

0 = x + (-x)

>> No.5313044
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5313044

>> No.5313067
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5313067

>>5313036
Really? I thought that shit was all Mario, you gain 1 but don't have 1 until you get a -1 then you just restart the level, meanwhile the entire time you're functioning on 0, but then that would imply that enviroment is just information and hence nothing...

Anybody know a formula that follows video game logic?

>> No.5313110

>>5309896
I lol'd.

>> No.5313114

>>5313067
Well you're initially functioning on 1 so gaining that -1 essentially is the thing that makes your previous journy 0... but then its the background of something always needs to be there so that 0, I guess you could say metaphorical whole, makes a real whole and thus the 1 and you get to keep koopa hopping

>> No.5313142

>>5313114
Well then you might as well always say youre functioning on 0 do to it being just a misdirection from the concept of a whole, that being said everything outside that 0 is actual while everything being manifested by the 0 is just information

>> No.5313150

>>5311559
i am equally prejudiced in that no numbers 'exist'

>> No.5313156

>>5313142
Yeah but by saying that you're insinuating that everything the 0 is being of or percieving is being calculated asjust information to it and thus is saying that the 0 is thinking of these 'actual' numbers as nothing

>> No.5313166

>>5313156
Well ofc it would 0 is the sum of everything outside of it!

>> No.5313201

I think this is one of the few /sci/ threads that could be archived

>> No.5313403

>>5309894
∑ (universe)

>> No.5314186

>>5313150
And I think that's a rational standpoint. I don't see a reason to favoritize any number or type of number over any other. They either all 'exist' ' or do not.

Which it is isn't deeply important to me.

>> No.5314201

>>5313150

What are numbers? For all I know, math is just a set of rules we gradually defined over time. It just happens that math uses these abstract entities named numbers as a tool.

>> No.5314211

>>5310161
But what if a is infinite? Then every finite number is zero! That doesn't make the slightest bit of sense.

So far I'm digging the cardinality of the empty set more than anything else, but it doesn't satisfy me either.

>> No.5314279

zero is a placeholder, to denote the lack of numbers :)

>> No.5314296

>>5314279
yea I'm pretty sure 0 is nothing aka the absence of something

yea Ill go with that

>> No.5314298

Group identity.

>> No.5314333

>>5314211
Infinity isn't a number.

Althoug you might say, neityher is zero.

>> No.5314342

>>5314298
What group?

>> No.5314343

0 = Shunya = Empty = Open = Potential

Zero is a potential number. It can be anything. The concept of Zero meant potential to early Indians who first used it in their calculations. It was there to show potential. It was later that the either Arabs or Europeans modified the meaning to mean nothing(nonexistent number). Possibly European because Europeans hated the Indian numbers. They didn't use it until much later. Even then they have always been vary of the number 0, negatives and decimals. Europeans considered these to be irrational and tried to ignore them for most of their history until very recently (less than 400 years or so).

>> No.5314346
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5314346

>>5314343
>le smart indians were so greart until teh horrible europeans did bad things and were so so dumb :)

>> No.5314350

Zero is not a number, but a concept designed to describe an abstract of nothing. You suck at maths if you don't know this shit. Before people start arguing at me or spouting shit about infinity go stab yourself in the eyes.

>> No.5314349

You might as well ask for the definition of what is the universe.

>> No.5314354

>>5314349
Why? Are you one of those edgy people who think zero is some super speshul thing which is impossible to define?

It's defined by it's definition in whatever context it is used, only an autist or a philosopher would look deeper than that, and neither of those are science/maths

>> No.5314351

A scalar value representing an empty set, as opposed to the philosophical concept of nothing, of which zero is something.

>> No.5314355
File: 615 KB, 220x165, wow-mom-pic.jpg.mxw220.ha.jpg [View same] [iqdb] [saucenao] [google]
5314355

1/3 = .333...

3 * 1/3 = 1

3 * .333... = 1

>> No.5314360

>>5314350
Zero is a number in some circumstances, and most people define it to be so

>> No.5314364

>>5314346
Don't take this the wrong way, I'm white as well. Its just the truth. Europe didn't use negative numbers till late 19th century or so. Zero wasn't in use till 18th century or so. Fibonacchi (11th century) made a case for the use of Indian number system with 0-9, but it was largely ignored. It wasn't until 16th century or so that it was a common usage. It was in 16th century or so when Europe first started using decimals. Europe was a backward country during that time. Arabs just had their Golden Period, India was on its second Golden Age. China was prospering with over 80 million citizen under its single empire. Europe was a fragmented state and largely feudalistic.

Don't take it as an attack on yourself, its an objective historical fact.

>> No.5314367

>>5314364
>its an objective historical fact.

then cite your sources

>> No.5314394

>>5314367
>>5314367
Cite sources for what? Negative number usage in Europe? (http://www.ma.utexas.edu/users/mks/326K/Negnos.html)) How fibonacci was ignored? (http://www-history.mcs.st-and.ac.uk/Biographies/Fibonacci.html)) Or how the Europeans of the time didn't consider 0 to be a number because of their greek-philia? (http://www.csun.edu/~hbund408/math%20history/math.htm)) Or how the modern european decimal system wasn't used commonly until around 16th-17th century or so? (http://school.maths.uwa.edu.au/~schultz/L11Stevin.html)) Or about historicity of Islamic Golden Age, Indian Golden Age, or China's population? Actually I made a mistake about China's population, its not 80 million, that was during 7th century. It was around 180 million at around 17th century. Or the feudalistic states of Europe and the fragmented states of Europe? The last few are basic world history. The early few are from history of math.

>> No.5314418

>>5314394
Get in the cloning machine. We need more like you.

>> No.5314908

Let V be a vector space. If there exists a vector v in V such that v + v = v, it is the zero vector.

>> No.5315992

If I had a cup, & this cup was empty, the space inside would be zero, but the cup would still exist, so thus when I filled the cup, gave representation to the space, the cup itself would be representing infinity.
So basically, zero is conceivably everything inside infinity, but then that leads to the question, are we inside the infinite or being it?
Follow mathmatical logic and we are within, follow reason and we are being.
This is not a paradox.

>> No.5315999

>>5315992
>Implying the cup and what is put inside arnt equal

>> No.5316063

>>5314394
Islam destroyed science in the middle east.

>> No.5316069

>>5316063
Yes and? It was also a propagator of science as well. Islam conquered other nations, then learned of their knowledge, then developed interest for science, then destroyed it when it conflicted with islam.

>> No.5316099

It is nothing, the equivalent of the absents of everything. From a math standpoint it means there is no (variable) there.

>> No.5316102

>>5316069
> then destroyed it when religious extremists took over.

FTFY

>> No.5316137

The amount of cats in a box with no cats in it.

>> No.5316687

After reading through the whole thread I have come to the conclusive answer that 0 is approximately equal to a distance above zero inside ones asshole do to the fact of any distance travelled into ones own asshole can be approximated of all distance travelled including any adjustments in direction or velocity of breaking down of the travelling dynamic and whence the journy is complete shall it be again compossed of that which it was before achieving mass in the asshole and thus be ready for the 'travel' again although one cannot say if it travelled at all do to the lack of anykind of observer

>> No.5316711

>>5309894
The sum of all finite integers.

What do I win?

>> No.5316712

How much wood a woodchuck can chuck.

>> No.5316731
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5316731

the final digit of my post number

>> No.5316743

>>5316731
But 1 is representative of infinity not 0 silly gook

>> No.5316755

1-1

>> No.5316791

the number n for which k+n=k

>> No.5316805

Zero is the division of rational number with infinity

>> No.5316816

>>5316805
CALCULUS>