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/sci/ - Science & Math

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11194774 No.11194774 [Reply] [Original] [archived.moe]

Hey nerds, /sp/ tourist here can you please tell me if zero is an odd or an even number or if it's the absence of value therefore neither?
Cheers doods, love you x

>> No.11194778

not a number you gimp

>> No.11194779

based. we really need to know guys. we're idiots.

>> No.11194780

It’s not a number, so it is niether even or odd.

>> No.11194783
File: 28 KB, 411x225, E38B4293-17EF-4128-9A10-D6EE0DA57D49.jpg [View same] [iqdb] [saucenao] [google] [report]

Thank you for confirming my suspicions everyone on /sp/ is retarded except me

>> No.11194784


>> No.11194785

This is so wrong.

>> No.11194791

0 is even, an even number has odd numbers on both sides of it on the number line. 0 has -1 on the left and 1 on the right. both odd numbers. QED 0 is even

>> No.11194816

Even number

>> No.11194817

even because it's divisible by 2

>> No.11194820

zero is a concept it does not exist

>> No.11194826

Literal retards, 0 is even.

>> No.11194828

wrong you want to know why zero is a circle? A circle represents the whole, the "beginning" and "end", except there is a no way to find out where the beginning and end is on a circle because there isn't one, it is an infinite cycle

>> No.11194830

Literal retard zero doesn't exist you fucking donkey

>> No.11194834

Yeah. Like you’ve got zero testosterone.

>> No.11194836

Get the fuck out tourists. You dont know shit about anything. Leave.

>> No.11194837

like you get zero pussy

>> No.11194843

>Letting women define your value system

>> No.11194845

>doesn't even know zero doesn't exist
>opinion on everything discarded as having no merit as it comes from the mind of a simpleton

>> No.11194869

It’s impossible for zero to be even or odd just because of the idea of zero. Even or odd is all about dividing by two, but you can’t really divide zero conceptually. Algebraicly you get zero, but it’s impossible to split nothing into different groups of nothing. You just get zero, more nothing.

>> No.11194870

why do you think we're fucking asking here, salty faggot?

>> No.11194878

go back to cte land

>> No.11194888

Numbers are used to count things and this is impossible without a signifier for 0, either for an absence of anything or to make multiples of 10.
It's weird because it's the opposite end of infinity.
Only autists don't regard it as a number (yes your math teacher is likely an autist)

>> No.11194903

A number represents value, there is no such value as zero in this reality, you only perceive an absence of value from a materialist standpoint because you can have "zero" computers, or zero apples. But what is a computer made of?

Steel, gold, silicone, etc etc when you destroy the computer those things are not gone, only what you made out of them, you didn't make a zero value out of it because that is impossible, first law of thermodynamics you didn't destroy it you only transformed it. Everything in this reality is made from the aether, there is never "zero" aether it can only be transformed into other objects you perceive as matter in the 3rd dimension. Only a materialist fool thinks zero is a number and not a material concept for convenience in accounting.

>> No.11194937

If zero is nether positive nor negative, then how could you expect it to be even or odd?

>> No.11194939

So zero is neither odd nor even?

>> No.11194942

>implying numbers other than zero are anything more than materialist concepts as well

>> No.11194945

No because it It doesn't exist, it can only appear to exist conceptually, it is not a real value outside of human perception

>> No.11194947

>not understanding what value is after it was explained in detail
Stop eating crayons

>> No.11194950

That means /sp/ was right, I think.

>> No.11194952

Well I take that back, it doesn't need human perception, it only needs 3 dimensions and the perception of something in that dimension to appear to exist.

>> No.11194959

the tldr is [first law of thermodynamics + (E=mc2} = no such thing as zero]

>> No.11195017

> he thinks numbers exist

>> No.11195030

I said numbers represent value, value exists you absolute mong incapable of reading compression on an elementary level

>> No.11195583

Most people in this thread are wrong.
An even number is a number which can be written as 2*n where n is an integer.
An odd number is likewise a number which can be written as 2*n-1 where n is an integer.
2*0 = 0, and 0 is an integer, therefore it is even.
Let us see if it is odd as well:
2n-1 = 0
2n = 1
n = 1/2
1/2 is NOT an integer, therefore the number 0 is strictly even.

>> No.11195598

hey idiot try and refute this then >>11194959

pro tip: you can't jack ass

>> No.11195612

Based and retarded

>> No.11196190
File: 2.66 MB, 1280x2104, NoZero.png [View same] [iqdb] [saucenao] [google] [report]

samefag here with a diagram for the simpletons

>> No.11196192

Even numbers are defined by the generating function of [math]{2x:x\in \mathbb{Z}\}[/math]

>> No.11196195

Missed a backslash
[math]\{2x:x\in \mathbb{Z}\}[/math]

>> No.11196214
File: 9 KB, 216x144, 0≠0.jpg [View same] [iqdb] [saucenao] [google] [report]

>zero is a concept it does not exist

Neither does one. Neither does any number. For example:

How many mountains in this picture? How many waters?

>> No.11196224

You have a herd of 20 sheep. You sell 10, you now have 10 sheep. 9 of your remaining sheep are killed by wolves, you now have only 1 sheep. This sheep dies of old age, how many sheep do you have?
The idea that 0 isn't a number is parroted by pseuds who literally don't think about it at even a surface level.

>> No.11196231
File: 68 KB, 1179x815, Vortex-Based-Mathematics.jpg [View same] [iqdb] [saucenao] [google] [report]

>Neither does one.

>Neither does any number. For example:

Well you bring up an interesting point since the all is "1" then one is the only real number in a way from the ultimate perspective, but that one can be and has been subsided infinite times so ultimately this is a psued argument. There are only 9 numbers that can be combined into infinite fractals

>> No.11196234

>The idea that 0 isn't a number is parroted by pseuds who literally don't think about it at even a surface level.

Says the psued that loves to "hear" himself speak but too dumb to listen to others "speak" (ie read the thread first). You have been proven wrong conclusively psued

>> No.11196241

All I've seen is low IQ shitflinging, the only people making points agree with me. Go back to watching niggers kick balloons or whatever it is you retards do.

>> No.11196243

>"1" then one is the only real number
It's not real, it's a+bi

>> No.11196245

thread stinks of highschoolers trying to sound smart. christ this board really is for the dogs these days.

>> No.11196247


>> No.11196250

>zero doesn’t exist
>is perfectly capable of typing it out on his keyboard

>> No.11196255

>All I've seen is low IQ shitflinging
>other ape tier droolers agree with me who cares you have proven me wrong conclusively I can't understand it therefore I will just pretend like it doesn't matter

Because you are too stupid to understand anything above your psued simple perspctive

>> No.11196256


Zero is a number and it is even. Any other answer is psudo-intellectual crap from people who want to waste time rather than doing anything useful.

Also, 0≠0

All numbers are ideas that exist in the human mind. They are useful tools, but should not be seen as an end in and of themselves.

>> No.11196259

You win stupidest post of the thread award congratulations. Anime is also real because your favorite hentai artist drew it, imbecile

>> No.11196262

This post is so ironic it's ferromegnetic

>> No.11196265

Sorry I have proven zero doesn't exist beyond any doubt I won't argue with you. Also shapes and distances exist which are values and I already covered this.

Reread the thread and take the time try to understand it or don't w/e

>> No.11196270

> it is all about dividing by two, but you can’t really divide 1.1 conceptually. Algebraicly you get 0.55, but it’s impossible to split 1.1 into different elements of the Rationals. You just get 0.55 more element of the Rationals.

>> No.11196271


>> No.11196273

You win dumbest newfag for not spotting bait

>> No.11196275

Correct answers:


>> No.11196277

Zero is a number and it's real, it's the number of times OP has had sex

>> No.11196278

>Sorry I have proven zero doesn't exist

You don't know what "proof" means. Just being stubborn isn't proof.

>> No.11196282

Just because you are not knowledgeable or smart enough to understand something doesn't mean it wasn't proven you wet brained donkey. Why are you on this board you trying to infect people with your stupidity?

>> No.11196283
File: 199 KB, 1000x1000, 1552739102025.png [View same] [iqdb] [saucenao] [google] [report]

By definition, zero is a real number because it's a member of the reals.

>> No.11196288


What is one minus one?

>> No.11196290

When anyone in this thread can refute this

Then post your proofs, til then stfu you hacks

>> No.11196294

>explained in detail
>absence of things doesn’t exist in reality
are you retarded dude? does the number pi not exist because you don’t see pi apples right in front of you?
Besides, the absence of stuff is very real. An Eigenstate of a particle has literally 0 probability density of other states. They are really not there thus 0.

>> No.11196295

Do you really expect this retard to understand that? He's just going to use the fact that he doesn't know what that is as some kind of refutation

>> No.11196296

if values exist then the value 0 does aswell

>> No.11196299

i have 0 pieces of chocolate in my mouth. it’s sad but true.

>> No.11196302
File: 12 KB, 300x259, bushfag.jpg [View same] [iqdb] [saucenao] [google] [report]


Waiting .... you will never refute this because you can't because you are no smart enough to even understand it not to mention it is conclusive which you are also not smart enough to understand

>> No.11196303

The thing about /sp/ is that they're all so retarded it's impossible to distinguish masterful shitposting from actual idiocy, and this thread is an excellent case study of this phenomenon.

>> No.11196309

if zero can't exist then I do have money right? Because the absence of it clearly is not possible.

>> No.11196314

Waiting ....

>> No.11196315

first law of td states temperature and thermal equilibrium exists. Irrellevant for the existence of 0.
e=mc^2 is first of all incomplete, and if I measure vacuum with no particle, what is its rest mass?

>> No.11196318

yes you have atleast one dollar, cool fact really

>> No.11196319
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>> No.11196326

got my thermodynamic laws confused. 2nd point is still valid

>> No.11196330

Let me explain i really simple for the cheap seats (though I already have in detail as well in this thread) since even a diagram for children couldn't work for you.

The first law of thermodynamics states energy never ceases to exist it inly changes form. Since all matter is energy (e=mc2) then that mans the matter is never gone, there is never a zero value in this reality because we are in closed system where the energy simply transforms into other things it is never "gone" never at a "zero" value, it can't be, it is impossible child. Therefore zero is only a concept that is useful in the illusory "reality" you perceive, it is not real, it can't be, it is only a CONCEPT. The lesson is over child, go do your homework now and stop arguing about things you cannot understand

>> No.11196336

>The first law of thermodynamics states energy never ceases to exist it inly changes form.

It DOESN'T say that energy has to be evenly distributed. That the universe as a whole has mass does not mean that parts of it can't be empty. The vacuum exists. Also, zero as a difference between two energy states is the GOAL of thermodynamics - heat tends towards equilibrium.

In an electrical circuit, if both sides have the same voltage potential, then no power will flow. Zero equals equality.

And finally, I asked this before and you ignored it:

What is one minus one.

If this question takes you paragraphs to explain, that doesn't mean that you are smart.

>> No.11196338

This is a really pedantic point but time symmetry breaks down over long periods so energy conservation isn't absolute

>> No.11196339

What is one minus one?

Being unable to answer this does not make you smart.

>> No.11196340
File: 18 KB, 480x360, texan2.jpg [View same] [iqdb] [saucenao] [google] [report]

bye simpleton

>> No.11196367

>a law isn't absolute
>it is called law specifically because it is absolute

spotted the psued

>> No.11196375

It was considered a law, and over any practical length of time it can be thought to be absolute, but it's not actually absolute.

>> No.11196378


> Responds to argument with nothing but name calling.

This is the closest you'll get to an admission of defeat on 4chan.

>> No.11196388

don’t call it admission of defeat, if you you can’t defend your standpoint, your intuition was wrong and you learned something.

>> No.11196395

>time symmetry breaks down over long periods
off topic, so sage
but how/why?
I get the time symmetry is not valid if the universal constants change over time, but are there measurements for that or is there another mechanism?

>> No.11196396

Explaining it is genuinely beyond my understanding at this point, but it has to do with inflation IIRC.

>> No.11196433

Questions like this are stupid because the answer just depends on how you define "even" and also how you define "zero". You can construct mathematical systems that say zero is even or zero is undefined. It doesn't matter as long as you are consistent. It's just semantic pedantry, not an actual mathematical question

>> No.11196468
File: 16 KB, 705x249, brainlets.png [View same] [iqdb] [saucenao] [google] [report]

Fuck all of you insolent children. Learn some math. Oh, and get the fuck off my board.

>> No.11196530

>vortex ”””””math”””””

>> No.11196546
File: 40 KB, 501x431, structure.jpg [View same] [iqdb] [saucenao] [google] [report]

>look at this hypothetical used in the 3rd dimension because he doesn't have the knowledge or intellect to understand things from a higher perspective more abstract than his tiny mind can process

>Still no one who can ever refute this >>11196190

Nah you get off my board you ape tier hack

>> No.11196560

Let me make it so simple any mentally retarded imbecile off the street can understand. When you can post proof that you find a way to destroy energy you come back to this thread and let us all know, then I will stop calling you and the rest of these donkeys imbeciles. Because then you will have proven you can actually have a zero value.

>> No.11196574

I'll even make it MORE simple for you dummies. Show me one time ANYTHING ever came form nothing. Are you seriously putting forth the idea that "something" can ever come "nothing". Because if you are, you are stupider than I thought as you can't even use elementary logic.

>> No.11196618
File: 34 KB, 769x733, 1560924243814.png [View same] [iqdb] [saucenao] [google] [report]

>this thread

>> No.11196620

assuming you are actually interested in the answer here's an argument for you.

we say a number n is even if it had the form 2k = n when k is an integer.

However it will help if we generalize the the term "even" to properly agree with our intention of the term. Now we can generalize this and say a similar statement about numbers realating to 3 or 5 or 7... etc. letting p be a prime number you can say a number is "even" with respect to p if there exists some k such that pk = n.

if you allow k to include 0 then for any p there exists a k such that n is 0. this statments since when k = 0 then for any p we have p0 = 0.

in this sense 0 is "even" with respect to 2 but also "even" with respect to any number.


>> No.11196623
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>> No.11196652
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anon wins, get off his board psueds

>> No.11196662

Based potato

>> No.11196773

It's four plus the empty set, I thought you'd know this

>> No.11196798


>> No.11196808

0 has yet to be formally defined in mathematics. We take it for granted because it makes our equations work.

>> No.11196810


>> No.11196816

This post sounds like it was written by a college kid who passed his calc 1 class with a B+ and thinks he's hot shit. You are absolutely wrong and to make it worse you're arrogant.

>> No.11196820

>not being exclusively interested in a function's behavior on [0,1]

>> No.11196821

you sound like you're being trolled

>> No.11196824

0 = virginity it's there but you can't do anything with it

>> No.11196825

I can't even tell anymore on this site man

>> No.11196826


>> No.11196828
File: 31 KB, 225x225, Snowpants.jpg [View same] [iqdb] [saucenao] [google] [report]

If zero ain't a number how come I get zero pussy?

>> No.11196831
File: 626 KB, 1773x1773, 1555871611189.png [View same] [iqdb] [saucenao] [google] [report]

If 0 is real why can't I divide by it? Checkmate atheists.

>> No.11196834

just assume you are

>> No.11196845

if an odd number is defined by an integer, n, such that 2n+1 is odd, then does there exist an integer n such that 2n+1 = 0?
NO. the only real number that is sufficient is -1/2 a rational number.
thus 0, which is divisible by 2, is even.
probably. I dunno, I'll asl your mom tonight when I fuck her with my cock. I'm literally e^x in that bitch.
based pianist.

>> No.11196847
File: 1.34 MB, 498x278, tenor.gif [View same] [iqdb] [saucenao] [google] [report]

NIHIGGGA i'll fuck your mom

>> No.11196852
File: 15 KB, 292x249, 2E27405F-2644-47FD-9BA8-7C0FBC880712.jpg [View same] [iqdb] [saucenao] [google] [report]

What does the word number... even mean?

>> No.11196862

a mathematical object

>> No.11196870

How do we market the word to the ignorant masses?

>> No.11196883

fuck you and your greasy fucking hands.
I will not have a pop sci invasion of mathematics, god dammit.
bad enough engineers think they are masters at math because they read GEB and took calc 3 in college.
Math doesn't and shouldn't exit its pure state EVER.

>> No.11196890
File: 347 KB, 623x351, panther.pdf.png [View same] [iqdb] [saucenao] [google] [report]

even and odd numbers alternate, and 0 is divisible by 2 to produce an integer. Its even

>> No.11196893

based autist

my mom was thinking out loud in numbers over thanksgiving it almost gave me a heart attack

>> No.11196897

what's the most complicated phenomenon that hinges on the evenness of 0?

>> No.11196901

if the real numbers doesn't include a number that is both even and odd at the same time doesn't that mean it has a hole?
your mom

>> No.11196903
File: 494 KB, 387x305, pepeWizard4.gif [View same] [iqdb] [saucenao] [google] [report]

uWu salty desu

>> No.11196913

>the real numbers doesn't include a number that is both even and odd at the same time doesn't that mean it has a hole?
by what principle?

>> No.11196980

In theory zero is even. But in practical reality it isn’t even or odd.

>> No.11197066

>But in practical reality it isn’t even or odd.
If zero wasn't even, then math wouldn't work. In actual, mathematical reality, zero is both even and odd at the same time. In fact it is both the most odd and the most even number, just like how it's the most rational number.

>> No.11197076
File: 1.64 MB, 300x300, 9code.gif [View same] [iqdb] [saucenao] [google] [report]


>> No.11197122

Wrong board. Numerology belongs on >>>/x/.
>inb4 something about Tesla, Rodin coils, and free energy.

>> No.11197143

thanks anon

>> No.11197148

>being too much a brainlet to understand simple math

this is the code to the entire matrix you pompous hack fool

>> No.11197569

it's just addition

>> No.11197831

>zero is a concept it does not exist
It is a number (counting up or down from it; doing math operations which result in it)
It is a concept (in computer science zero represents 'false', non-zero 'true'; it's one or the other; there is no 'maybe'...)

>> No.11197836

And yet you can't understand it.

>> No.11197843 [DELETED] 

>No because it It doesn't exist...
You're confusing 'null' with zero. They are mutually exclusive.

>> No.11197858

>If 0 is real why can't I divide by it?
Because you flunked 1st grade math, muh niggah.

>> No.11197863

>No because it It doesn't exist...
You're confusing zero with 'null.' They are mutually exclusive.

>> No.11197916

I think people are forgetting it’s just your opinion. Zero could be even, odd, both, or neither. There isn’t one right answer.

>> No.11197928

>Zero is even because Peano says so!
How very unscientific of you.

>> No.11197951

0 is even and it's pretty easy to understand why.
Take any integer and stack up that many pancakes into two stacks, alternating stacks for each pancake. So, left, right, left, right, left, right, etc.
If you run out of pancakes and your stacks are the same height, you had an even number of pancakes.
If you run out and one stack is one pancake higher than the other, the initial number of pancakes was odd.
If you run out and one stack is a fractional number of pancakes higher than the other, you didn't have an integer number of pancakes to begin with.
If you run out of pancakes and wind up with any other scenario, i.e. one stack is two or more pancakes higher than the other or you have more than two stacks, then you did it wrong, try again dumbass.
If you don't run out of pancakes, then your number is the cardinality of an infinite set, and therefore not actually a number.
If you run out of pancakes and your stacks are the same height, but they're not the same width (or they are the same width but they're wider than when you started) then you forgot to cook your batter.
Now try this with the integer 0. That is, start with 0 pancakes.
You've now run out of pancakes before you've even begun sorting them into stacks.
Compare the height of your two empty stacks of pancakes.
Since they're both empty, they're the same height (empty).
Therefore, 0 is even, QED.

>> No.11197952


>> No.11198047
File: 195 KB, 890x670, FoCpG.jpg [View same] [iqdb] [saucenao] [google] [report]

>> No.11198096


>> No.11198097

Thanks for convincing me it's time to leave this board.

>> No.11198120

math isn't a science, it's its own group from philosophy.
The "scientific method" generally isn't relevant. Say what you want to, but prove it is how mathematicians go.
Axioms are the basis of the structure of a mathematical universe, they are required to be true.
>now let me use it, inappropriately, in my own dogmatic way to generate shitty models and then blame math when it goes wrong.
>hurr durr i ama science boy but don't understand philosophy or what science even means.
>philosophy is GGGAAYAYA

>> No.11198346

if nothing != something then it is elementary logic that something != nothing as anon said, are there people on this board that honestly can't understand this

>> No.11198363

math is also an abstract concept and not always applicable to reality, you can lie with number just as you can with words.I know you thought you were clever with your post but you weren't you just showed how ignorant you are once again.

“Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.” - Nikola Tesla

>> No.11198435

uh no anon good boy points for CS weigh in though

>> No.11198437

none of this is relevant to this conversation anon

>> No.11198560

>uh no anon...
My, what a convincing counterargument!
Thank you for demonstrating your expertise and sharing your in-depth knowledge of the subject. I'm sure everyone has benefited.

>> No.11198580 [DELETED] 

>none of this is relevant...
Sure. None of it is relevant to the strange reality YOU live in. But, then again, few geniuses are recognized in their time, am I right? Certainly, you fall into this category. Yes, I'm certain of it.

Nonetheless, the denizens of /sci/ thank you for bestowing your brilliance in the matter. Certainly, all mathematicians will benefit from this astounding discovery, and your unrivaled lucidity in communicating it will not go unrecognized...

>> No.11198587

>none of this is relevant...
Sure. None of it is relevant to the strange reality YOU live in. But, then again, few geniuses are recognized in their time, am I right? Certainly, you fall into this category. Yes, I'm certain of it.

Nonetheless, the denizens of /sci/ thank you for bestowing your brilliance in the matter. Certainly, all mathematicians will benefit from this astounding discovery, and your unrivaled lucidity in communicating it will not go unnoticed...

>> No.11198591

Based and CS pilled

>> No.11198628


Don't tell me... and the Earth is flat, too?

>> No.11198656

Whoever wrote this must be new to programming.

1. Code does not define a RANGE of values to be entered, then tests and flags if number is outside of said range (i.e. "Enter an integer between 0 and 100:").

2. Code makes assumption that zero is even from the outset. There is no algorithm performing a test. Instead, it is a long, awkward 'if' statement.

You're not showing off. You're showing us you don't know what you're doing yet...

>> No.11198657

>Thank you for demonstrating your expertise and sharing your in-depth knowledge of the subject.

Yah I did anon I am the poster in this thread that actually knows what they are talking about and posted all the evidence unlike you.

butthurt cope, indeed I did do those things, I gave the equation none of you understood that was obvious once you do and none of you can ever "solve" because there is no solution because there is no such value period. Stay mad psued

>> No.11198664 [DELETED] 

You're just some antagonist little twit looking to stir up some nonsensical shit for your own amusement.

So, what happened? Teacher gave you a zero on your last math test and you're trying to argue that zeroes don't exist?

GTFO, loser...

>> No.11198666

You're just some antagonistic little twit looking to stir up some nonsensical shit for your own amusement.

So, what happened? Teacher gave you a zero on your last math test and you're trying to argue that zeroes don't exist?

GTFO, loser...

>> No.11198672

seething brainlet cope, salty desu yummy

>> No.11198680

>Based and CS pilled
Kek. Hardly...

>> No.11198697

>Correct answers:

"Correct" becuz they're all shitposted by the same mischievous, antagonist OP...

Like I said, GTFO !

>> No.11198764
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>> No.11198776

fucking literally this.
half these niggas don't know what a proof is.
>Nikola Tesla
can you please reproduce this post?

>> No.11198860


>says a literal retard psued monkey who can't use simple logic

Do you think anyone finds you credible desu? They are laughing at you not with you

>> No.11198863

learn to use a switch nigga

>> No.11199007

Lmao >>11197122 called it. You don’t have special insider knowledge about the “structure of reality” because you know about some arbitrary integer sequence, you’re a pseud that cannot into actual mathematics. Next you’ll start talking about how we’re all just too simple minded to understand your profound sequence. You don’t belong here, you’re lost.

>> No.11199025


Number entered: 102

Result: "Your number is odd!"

Boss: "You're fired."

>> No.11199097

>moronic person says moronic things

imagine my shock, how novel

>> No.11199988
File: 79 KB, 1000x472, Screen Shot 2019-12-04 at 8.17.12 PM.png [View same] [iqdb] [saucenao] [google] [report]

Nice b8

>> No.11200364

>Numbers are used to count things and this is impossible without a signifier for 0
Simply incorrect.

>> No.11200650

nice argument

>> No.11200975


>> No.11201032

Y'know, I remember seeing a maths journal where every single paper, every last one, used different definitions of even and odd. Every single one. None of them used a universal definition of even and odd defined from their first year of study. Absolutely not a one of them. They all were the living definition of hacks trying to write their own version of perfectly functional number theory.

>> No.11201036

Retard, show me the plank that has length i and then try describe quantum mechanics without complex valued functions.

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