/sci/ - Science & Math

>>14839043
Define number y such that y^2 = 2. There, problem solved.

1.4142135623730951

>it's another episode of brainlet not distinguishing between abstract mathematical existence and physical existence
You will never be a mathematician and you will never be a philosopher.

>>14839043
>another irrational number thread

>>14839043
>le heckin' numberinoooos are scribbles on a paper
Medsnow.

>write it down
[math]\sqrt{2}[/math]
Done. Next question?

>>14839060
How can you say it exists when you can’t even conceptualize it properly? It’s neither observed nor comprehended with the mind. You’re just imagining that it does exist, like God

>>14839100
>if you can't express something in the form of heckin' decimal digits you can't conceptualize it properly
>t. an actual NPC

>>14839043
Take the quotient
[eqn] \mathbb{Q}[x]/((x^2 - 2)\mathbb{Q}[x]) [/eqn]
then you have a number with that property.

>>14839104
Ive never seen sqrt(2) nor have I fully conceptualized the number. Neither have you. You’re the NPC here. It’s a useful concept in approximations, but there’s no need to go full Platonic forms

>>14839043
> t. pythagoras

>>14839110
>Ive never seen sqrt(2)
You're never seen a 1 either, mouth breather. Numbers are abstractions.

>>14839060
>it's another episode of brainlet not distinguishing between abstract mathematical existence and physical existence
What is 1/0?

>>14839043
Define "number."
sqrt(2) is the obvious answer, so I'm guessing you have some personal rule against counting it like "irrational numbers aren't numbers."

>>14839152
If I can't count it on my fingers, I can't conceptualize it and therefore it's not a number.

>>14839100
>nor comprehended with the mind
It's easily comprehended if your IQ is sufficiently high, brainlet.

>>14839043
Sqrt(2)

>>14839152
>Define "number."
A quantity represented by a numeral

1 in base sqrt 2

Yes there is.
It's 2.5.
>Source?
I just completely made it up..

>>14839173
1 in any base is 1.

>>14839059
This.

>>14839182
Sorry of course I meant 10

>"NOOOOOOO YOU ARE NOT ALLOWED TO HAVE A COMPLETE ORDERED FIELD NUMBERS HAVE AN INFINITE AMOUNT OF GAPS IN THEM WHAT DO YOU MEAN BY CONTINUITY EVERYTHING IS A BUNCH OF PIXELS THINGS CANT BE SMOOTH AND COMPLETE THEY JUST CANT OKAY????"

>>14839246
A curve is not a collection of infinite points, but rather a law on which to construct points. There isn’t always a y-intercept. I hope this revelation doesn’t make you shit your pants

>>14839043
ITT: How can you say you are dumb with saying dumb?

>A CRUVE IS NOT A COLLECTION OF POINTS!!
>IT'S JUST NOT, OKAY?!?!?! IT'S JUST NO!!!
People who have given up on the prospect of ever contributing anything meaningful to mathematics are forced into a lifetime of mindless contrarianism. Sad.

>>14839168
What's a numeral?

>>14839110
>Ive never seen sqrt(2)
Have you seen a square?

>>14839263
A symbol that represents a number.

>>14839300
>a number is a quantity represented by a symbol that represents a quantity represented by a symbol that represents a quantity represented by a symbol that represents a...
Well done, mouth breather.

>>14839156
>ability to count up to 21
based

>>14839302
do you deny writing as such, mouthbreather? a vowel is a sound represented by a letter that represents a vowel represented by a letter etc.
I want Mandelbaur back.

>>14839326
fuck, friendly fire. I aimed at >>14839300

>>14839326
I don't know what your verbal vomit is about. I'm going by your own definition. So what's at the bottom of your infinite regression? How do I know what a number is? :^(

>>14839060
>it's another episode of brainlet not distinguishing between abstract mathematical existence and physical existence
>mathematical existence
Numbers are a description you illiterate.

>You will never be a mathematician and you will never be a philosopher.
And no mathematician will ever answer OP's question with an actual quantity. Only a philosopher is ever going to tell you why it's not answerable (because it's not a quantity for math to describe)

>>14839076
>a fancy symbol
Okay, what is the quantity? Are you sure this isn't a contradiction to math itself? Mathematician, are you okay?

>>14839064
>irrational
>number
Lolno

>>14839110
>number
No

>>14839132
Undefined. Because 0 is not a number

>>14839355
Low IQ wordcels go on /lit/.

>>14839355
>>irrational
>>number
>Lolno
Why not?
>Undefined. Because 0 is not a number
oh, you're just a contrarian

>>14839375
>oh, you're just a contrarian
No, it's just that when you write
>[SYMBOL]
>[EXPRESSION]
>placeholder for [NO QUANTITY]

it still doesn't make it a quantity. How the fuck am I supposed to do math when I don't have a fucking quantity to work with? I bet you don't even want to think about that because it means dwelling into the realms of philosophical explanations (because there's no fucking quantity to apply math to for a mathematical explanation).

>>14839389
What's a quantity, according to 105 IQ virgin wordcels?

>>14839389
You can pass around the numeral for sqrt(2) in the same way you can with any rational number. There's no problem philosophically or mathematically
>>14839394
wordcels are smarter than you

>>14839398
>i am v-v-very smart!!
Then you should be able to define "quantity" for me, virgin.

>>14839402
I've also fucked more women than you

>>14839394
>define define define
>logomachy please!
>semantic bullshit over what can't be argued over

All of which would have worked for you if what we were talking about was definable in the first place. But it isn't. So no matter how I define it for you it's not going to make a difference.

>>14839398
>You can pass around the numeral for sqrt(2)
>in the same way you can with any rational number.

>numeral
>number

Stop contradiction yourself.

>>14839413
The numeral [math]\sqrt{2}[/math] represents a number just like the numeral 2 represents a number.

>>14839413
>ummm X is not a quantity!!
>what's a quantity?
>ummm that's not definable
Why isn't trash like this getting banned?

>>14839420
the implied requirement was this to be a base 10 notation. you failed according to tricky OP

>>14839389
>How the fuck am I supposed to do math
Worked fine for the billion other people who do math with irrational numbers routinely.
Why should we care about your personal limitations?
None of this finitism retardation ever seems to lead to new answers for the problems you want to use different symbols to expresss.
What's the point if you don't produce anything new? Why not just skip the autistic detour and use the existing infinity based methods?

>>14839043
you shouldn't be fucking so hard with us, sir. there might be some resentment as the result.

>>14839431
OP is a poopoopants

>>14839420
>The numeral 2√ represents a number
No it doesn't. It represents "undefined". Were it an actual number then you would have posted an actual number

>>14839423
>Why isn't trash like this getting banned?
Read this proof again>>14839355

If I defined the square root of two then it would literally contradict math itself. I'm not doing it for the benefits of math. If the janny really wanted to solve the problem then they would go full pythagoras and have people like you thrown into the Mediterranean for insisting that math works like a hooker on crack.

>>14839432
Worked fine for the billion other people who do math with irrational numbers routinely.
No it didn't! Case in point; the fact we're still talking about it and the fact you're still writing "root two" instead of the actual quantity.

>Why should we care about your personal limitations?
Mine? You mean maths.

>>14839443
I accept your full concession, wordcel trash.

>>14839443
>No it doesn't. It represents "undefined". Were it an actual number then you would have posted an actual number
It does not represent "undefined", it represents a number just like 2 does. [math]\sqrt{2}[/math] is a numeral that represents an actual number just like 2 is a numeral that represents an actual number.
>If I defined the square root of two then it would literally contradict math itself
How?

>>14839443
Curious as a neutral party, how many years of math education have you gotten?

>>14839445
>this incel again
stop posting already lol you've lost every argument you've gotten into and you're not helping this one either

>>14839254
>law on which to construct points
That's how you draw a curve, not what the curve itself is.

>>14839355
Yes, it's not rational, but it being irrational does not imply that it is not a number at all.

>>14839431
>the implied requirement was this to be a base 10 notation
Protip: It doesn't matter what base you use because the problem persists in all of them.

>>14839445
>I accept your full concession
You bots need a new phrase.

>>14839452
It does not represent "undefined",
It is specifically used as a symbol/expression because of such
>it represents a number just like 2 does.
2 is quantified. 1.14.....I can't even tell you the quantity you see? It's undefined. I can estimate and use symbols, but that's simply a glorified coping mechanism.

>How?
Re read the post I quoted.

>>14839455
>quantify your education pls
For the benefit of all the alleged mathematicians I'm schooling right now, I won't.

>>14839472
>but it being irrational does not imply that it is not a number at all.
Does it not though? You cannot determine the quantity and a "quantity" refers to a SPECIFIED AMOUNT. The amount here is never "specifiable", it cannot even be used as a number is.

>>14839486
Why is using the numeral [math]sqrt{2}[/math] to represent the irrational number [math]sqrt{2}[/math] a coping mechanism, but using the numeral 2 to represent the number 2 not a coping mechanism?
Why do the integers exist, but the irrational numbers not exist?

>>14839493
whoops I used the wrong slash

>>14839486
>doesn't matter what base you use
why do I need a base?

There is no number which satisfies the property 3x=1. If you believe there is, please write it down.

>>14839493
>the irrational numbers not exist
Heisenberg principle

>>14839197
>>14839059

>>14839508
wtf are you talking about

>>14839493
>Why is using the numeral sqrt2 to represent the irrational number sqrt2 a coping mechanism, but using the numeral 2 to represent the number 2 not a coping mechanism?
>Why do the integers exist, but the irrational numbers not exist?

Using the ORIGINAL axioms of math(arithmetic), "2" can be determined but using the same axioms "root 2" cannot be determined as number. It is only through the introduction of "special snowflake exceptions" and more and more axioms that irrationals are equated to "number". They are not "of number" and never could be no matter how much math you apply to them. They tried and failed, they could not actually use the existing numbers conjured to finish expressing it.

How do you determine the property of a number when you can't determine the number in the first place? You cannot: therefore it is not math. It's not number, it breaks number. That's why it is extraordinarily important that you mathematicians not treat it like one. We wouldn't want you wasting your effort for thousands of years to no avail calculating what contradicts the methodologies you employ.


>>14839502
>why do I need a base?
Just use the object itself. You know, like plant phyllotaxis.

>>14839523
>wtf
the reality can not be used to represent irrational numbers. Unlike rational numbers, it is purely an abstract concept. what is so difficult about it?

>>14839534
>We wouldn't want you wasting your effort for thousands of years to no avail

>>14839542
we need the entire set of real numbers to model almost everything in physics
attempts at discretization have all failed

>>14839542
>the reality can not be used to represent irrational numbers.
If rationals exist, then the diagonal of a unit square is an irrational number

>>14839548
>we need
try harder

>>14839567
>the diagonal of a unit square
sounds very abstract. is this an approximation of a real distance?

>>14839567
>the diagonal of a unit square is an irrational number
The diagonal of a unit square doesn't have a heckin' lengtherino. Prove me wrong. :^)

>>14839579
>the diagonal of a unit square
>sounds very abstract. is this an approximation of a real distance

>>14839567
this completely disproves the rationalist ideology

>>14839461
I don't know what you're refering to but I guess I'm not surprised a literal subhuman who thinks he's "winning" with his denying rational numbers thinks he's "winning" while getting stomped in other threads. You are mentally ill.

>>14839579
No, it's the exact value of a real distance. Take a unit square. Now take the diagonal of that unit square. Now lay that diagonal down on a real number line with one endpoint at zero. The other endpoint will land EXACTLY on root two.

>>14839579
these are the people telling you irrationals don't exist

>>14839670
I blame the metric system. A whole generation of kids have been brought up to think that exact powers of ten are somehow magical.

>please write it down.
>[math]\pm\sqrt{2}[/math]
>not knowing the difference between numbers and numerals

>>14839355
this is the standard proof taught to pre-pubes. The problem is that is p/q have no common factors, that automatically makes them IDENTICAL with p/q that both have the same common factor. Two things that are equal are not contradictory.2/3 == 4/6.

>>14839355
>a fancy symbol

All of math is nothing but fancy symbols

holy shit what a heated thread. Great job OP

>>14839670
>irrationals don't exist
they do not exist in reality. anything we can measure is approximate and subject to measurement errors. is this such a hard concept to grasp?

>>14840776
Every circle has a π in it.

>>14840787
where can such a thing be obtained? any two physical circles will differ if examined carefully.

>>14840792
Oh great, another smoothbrain who's never heard of Plato. Things don't have to be tangible to be real. The universe isn't limited to stuff you can lick.

>>14839066
/thread

>>14839521
That's a floating point error

>>14840795
>The universe isn't limited to stuff you can lick.
True, however the OP request is.

>>14839043
what if i just create a new number line that's orthogonal to the real number line with the property that
transcendental * transcendental = rational

>>14840838
No it's not. He asked for somebody to write down root two. Which you can write down as "root two," because that's the name of that number.

>>14840843
I think you mean irrational. Transcendental numbers are non-algebraic. And the problem with your idea is that irrational times irrational is always irrational.

>>14840851
> irrational times irrational is always irrational.
>square root of 2 * square root of 2 is irrational
middle school dropouts should stay out of /sci/

>>14839043
The "number" x is a function. Since the function is infinite this "number" cannot exist in the real world. We say that as the decimals of this function approach infinity the function will approach some value "sqrt(2)". In reality we can only give approximations to this value. Nonetheless there is still a "limit" of this function which exists and that is what we are referring to when we say "sqrt(2)".

>All of math is nothing but fancy symbols
Math is the language of quantification. Much like any other language these "symbols/words" are used to represent something that has meaning, only with math the meaning is purely quantitative. Using a symbol to represent something that was never determined by math to be an actual quantity is like using a word in another language that doesn't refer to a thing, action or... anything at all, not even "nothing".

Meanings/words sometimes don't translate or mix/match well when translating from one language to another, in the case of math and "root 2" the English word "undetermined" has to come in because the language of quantification can't complete its "sentence" using numbers. Much like the English language has difficulty with double negatives.

>>14840776
Nope, if rationals exist irl by your admission then you can precisely construct a unit square and have an exact irrational

>>14839043
Numbers are not real
2 doesn't exist as well

>>14839043
[math]
x^2 = 2\\
2 * ln(x) = ln(2)\\
exp(ln(x)) = exp(ln(2) / 2)\\
x = exp(ln(2) / 2) = sqrt(2) = 1.4142 ...\\
[/math]

>>14839302
YWNBAN

>>14839521
the snake is lying

[math]\sqrt{2}[/math]

>>14839043
({ x in Q | x^2 < 2 },{x in Q | x^2 >= 2})
^ original invention, do not steal

>>14839043
[math]-\sqrt{2}[/math]

>>14840849
nice. i have written down the number 1/0. what do you think of that?

>>14841838
point at infinity, I guess

>>14839043
There is no state of Ohio. If you believe there is, please write it down.

>>14841838
That's an undefined expression.

>>14841894
no, it is the number 1/0. i wrote it down, so "1/0" is its name

>>14842049
>no, it is the number 1/banana. i wrote it down, so "1/banana" is its name

>>14842083
yes

>>14839355
>where we may assume
what if we cant assume?

>>14839355
Here
I'm showing you the square root of 2 "in the real world"
Now shut the fuck up
>inb4 "but the triangle is not 100% accurately drawn so that's not actually the square root of 2"
I'm too lazy to hop onto a CAD program and do it there but you can draw a triangle with sides equal to 1cm, engrave it on a plate using a CNC machine and enjoy your triangle with one side equal to sqrt(2) cm

>>14842181
Man this board has gone to shit so much that engineegers are now btfo’ing people in math threads

>>14842181
Doesn't prove anything. Who said the hypotenuse has a well-defined length?

>>14842253
You can measure it with a ruler, smoothbrain.

>>14842181
>equal
impossible. how would you verify the accuracy of your statement? also if you CNC a second triangle, it will differ from the first. there is this thing called precision or tolerance

>>14842257
>You can measure it with a ruler
I can and it certainly won't be sqrt(2).

>>14842257
with what accuracy, braindead?

>>14842253
>Who said the hypotenuse has a well-defined length?
Pythagoras of Samos

>>14842239
Math has seen better days in /sci/

>>14842181
One could argue that it is physically impossible to draw a perfect triangle with one side equal to sqrt(2) cm.
For that matter, no precise triangle could ever be created in the real world since no matter how precise your instrument is, there will ALWAYS be an infinitesimally small degree of error.
It's beautiful how math is interconnected, in this example:
Just as we will never reach the exact value of sqrt(2), we will never be able to accurately draw an isosceles triangle in the real world.
That doesn't mean that the concept does not exist, it's just that it cannot be rendered precisely in the real world.
But it does not matter if it cannot be rendered into the real world, because mathematical concepts, even if they are ideal, still hold together the fundemental laws of our universe and all of its interactions.

>>14842262
Prove that it does.

>>14842264
Prove that the hypotenuse has a well-defined side-length without circular reasoning. Protip: you literally can't.

See dedekind-completeness

>>14842266
>>14842269
>"Prove one of the most proven theorems in mathematics"

>>14842271
You sound literally retarded.

>>14842270
based and robust

>>14842271
too bad we can not construct pythagorean triangles in reality. as a matter of fact, we can not construct anything with absolute precision. are /scifags/ not aware of this limitation of our universe?

>>14842282
You sound literally retarded just like him.

I cannot create an isosceles triangle in the real world, but it does not mean that the concept does not exist...
I can create one in the ideal mathematical though.
You are confusing real physical objects with abstract ones.
The rules that create these abstract objects do have an impact on the real world, even if those abstract objects cannot be created in the real world

>>14842287
Prove that the hypotenuse has a well-defined side-length without circular reasoning. Protip: you literally can't.

>>14842282
>we can not construct anything with absolute precision
Define absolute precision please

Y'all motherfuckers need Plato.

>>14842287
>even if those abstract objects cannot be created in the real world
not even when using a pen to write them down like the OP wanted?

>>14842294
The opposite of infinitesimal

>>14842298
Ok, now define infinitesimal in terms different from "the opposite of absolute" or any other circular reasoning of the kind

>>14842296
When you use a pen you merely create a symbol of the abstract concept.
Also, what would constitute the triangle in your drawing? The atoms of the ink?
In that case you would not be creating an ideal triangle but merely a collection of atoms that are not even shaped like a perfect triangle if you look at them on the molecular level.

>>14842300
more precise than we can measure
will that work for you?

>>14839326
>vowel is a sound represented by a letter
a vowel is both a word that identifies a subset of sounds a certain language's speakers emit and a word that identifies the letters corresponding to said sounds.
There is nothing circular about it, pseud.

>>14842300
Ok let's say that absolute means an ideal point, something that cannot be further divided into smaller chunks

>>14839534
>the original axioms of maths
LOOOOL LOOKS AT DIS NIGGA!

>>14842306
my point exactly, abstract concepts can not be represented by real objects. we need context for that

>>14842307
>>14842311
65 combined IQ
Some of the worst definitions I've ever seen.

>>14842316
That was my entire point since I entered the discussion.
For reference, I made these replies
>>14842264
>>14842287
>>14842306
>>14842298
>>14842311

>>14839108
This but the Wildberger fanboys aren't ready for this

>>14842324
Well maybe I wasn't very rigorous in the use of my vocabulary ahaha, English is not my first language

Irrational numbers don't exist in reality, we don't have infinite measuring precision.
Rational numbers don't exist in reality, you can't perfectly cut 3/4 of an apple.
Integers don't exist in reality, show me -1 of something.
Naturals don't exist, what constitutes "one" thing is entirely subjective. Atoms are the ultimate unit? Wrong, now it's quarks and god knows what will lie ahead.

>>14842351
>Rational numbers don't exist in reality, you can't perfectly cut 3/4 of an apple.
LOL. What a mouth-breathing imbecile.

>>14839108
The funniest part about this thread is that all of the Wildberger fanboys know so little math that they don't even understand that their question is easily answered by field extensions and Galois theory that most undergraduate math majors have seen. (Note how this post has zero replies attempting to refute it.)

If you're going to critique the existence of real numbers, at least talk about something that's a little philosophically worrying, such as the existence of a real numbet that can never be defined (in fact, there are uncountably many real numbers that can never be defined; see https://arxiv.org/abs/math/0411418).). Instead, you're just lobbing us softballs by screaming about how a perfectly well-defined and constructible number doesn't actually exist. It really shows just how little math all of the finitists on /sci/ actually know.

>>14842362
>65 combined IQ
the world of finance enters the chat

>>14842372
>lobbing us softballs
t. never've been outside

>>14842374
You are quite literally subhuman.

>>14842377
Explain how I'm wrong then :)

>>14842377
Based, stop doing math, go outside

>>14842388
>Explain how I'm wrong then :)
easy, how much do you bench? + post body

>>14842377
>>14842382
>>14842388
>>14842394
Do homework and shut the fuck up

>>14842399

>>14842399
Please tell me more how you can't have exactly 3/4ths of something because you can't cut an apple precisely, you actual mouth-breathing subhuman.

>>14842411
you can have 3/4 of 4

>>14842362
show me 3/4 of an apple, I'll wait

>>14842410
Shut the fuck up worthless little kid

>>14842415
Why do I need to show you 3/4ths of an apple, mouth breathing subhuman?

>>14842398
lmao
Nigga been real quiet after this one

>>14842415
show me 1/4 of an apple first

>>14839043
The consensus so far is - the number exists but can not be represented in reality. Can we move on now?

>>14842448
>cannot be represented in reality
>exists

>>14842491
does infinity exist, dear materialist?

>>14842508
Of course not

>>14842418
you're the one saying rational numbers hekkin exist

>>14842562
Yes. What does cutting apples have to do with this, clinical subhuman?

>>14842294
Sadly, I can't definite it with absolute precision

>>14842569
if they exist in the real world then find me an example of 3/4 of something

>>14839043
there is a real analysis proof that it exist I too one questioned that if numbers of decimal expansion keep on going forever how do we know it exist. It is one of most beautiful proof for me I am too retarded to understand it but before proving root 2 exist we prove 2 is less than 4 and that was really beautiful. And I know you are a troll but this is for anyone who wants to look into it more rigorous proof.

>>14842608
>find me an example of 3/4 of something
I punch your mother 3 times in the womb for spawning you and then punch you 1 time for existing. Your mother will have received precisely 3/4ths of my punches.

>>14839043
>if you can't write it down it doesn't exist
I thought this board was the cream of the white masterrace?
t. black

>>14839436
Am I stupid or is this correct

>original is $30
>should've only been $25
>they each should've only paid 8.33 then
>bussboy doesn't return $2, the bussboy does give them 1$ back each though
>8.33 + 1 = 9.33
>(9.33 x 3) + 2 = 30

>>14842677
what is a punch exactly? is it an objective definition?

>>14839436
Owner has $25, bellboy has $2, men have 3 x $1. What missing dollar?

>Socrates respawned and is wandering around /sci/ - the thread

>>14842759
What a desperate attempt to save face.

>>14842866
>save face
unlike you I have studied basic set theory so I know the lengths we have to go to formally define what a number is.
if you can't formally define what a punch is then we can't say "3 punches", there might be more or there might be none

>>14842891
Your absolute desperation is palpable.

>>14839100
>How can you say it exists when you can’t even conceptualize it properly?
I can conceptualize it properly. It's just a partition of the reals into two sets based on the property x^2 = 2.

>>14842901
thanks for conceding that not even natural numbers exist in the real world, it has been a pleasure

>>14839076
Answers bait question . Leaves .
Chad .

>>14843036
Thanks for conceding that you're a total mouth breather. Rational numbers clearly correspond to quantitative relationships in reality.
>b-b-but you d-d-didn't define what a heckin' punch is
Why would I need to? How mentally challenged are you?

>>14839043
https://upload.wikimedia.org/wikipedia/commons/5/5c/Isosceles_right_triangle_with_legs_length_1.svg

>>14842294
>Define absolute precision please

And that's the beauty of it.

stop fucking arguing about precision or if something exists

you're not making a profound point by saying "well right triangles do not exist because we could never make something that precise..." or "i cant count sqrt(2) on my finger so it isnt real...." you fucking idiot math is not a physical science, it is not MADE to describe real things with precision. get that through your thick skull

math is a formal science that is concerned with logic, just like CS. nobody says "well binary lists don't exist in the real world, so computer science is fake!!!" you must have autism and severe iodine deficiency. math is a science of logic, not of the physical world. saying "well...math only makes sense logically, it's not real!!!" is like saying that physics describes the universe. ok? that's the point? please graduate highschool and get off of /sci/ if your IQ is less than 50

HAVE YOU FUCKERS REALLY NEVER HEARD OF PLATO?

>>14843466
>stop fucking arguing about precision or if something exists
what part of 'write it down' do you not understand?

>>14843481
[math]\sqrt{2}[/math]
There. I wrote it down.

>>14843530
well, thank you. so what was this whole fuss about?

>>14843532
Oh y'know. Just a bad case of the Mondays.

>>14843466
midwit post, belonging right in the middle of the inverted bell curve

>>14842333
I mean, I think wilberger is as schizo as everyone else, but he has talked about constructive field extensions before, and he says he doesn't have a problem with it.

>>14842713
the trick is that the last addition makes no sense in the context
it's just there to confuse and it's meaningless

>>14839059
I call it 1.4. Take it or leave it.

>>14839108
>>14842372
ok except its literally called irrational because it doesn't make any rational sense because its all fake though

>>14839389
pic descends into pure strawman by the 2nd line

>>14842260
if the sides of the triangle are actually length 1 and you connect them with a line, then the line is really there, what doesn't exist is your measurement

>>14839110
squirt 2

>what is the square root of 2, don't say √2, give me a real answer
What's with all this philosophy bullshit

>>14839043
42

>>14846904
>what is the square root of a banana?
>[math] \sqrt{banana}[/math] of course!

>There is no number which satisfies the property x^2 = 2.
OP leaves the sense of existence and number being used implicit. Natural language is always ambiguous, but in this case the ambiguity is significant enough to lead to seemingly contradictory conclusions. When presented with such a question, one can simply consider each sense separately.

Suppose existence is defined as being a physical object and numbers are taken to be abstract, non-physical objects. Then no numbers exist.

But we can also take existence to mean that we can construct a proof of the existence (in the usual mathematical sense) of an abstract mathematical object using some axioms and rules of inference. In this case the existence of the square root of two is also uncontroversial.

Alternatively OP may be using a personal definition of existence and number, but if so OP should have mentioned it and so should anyone answering OP’s question.

>>14839043
Depends on how retarded your definition of "is" is. [math]x^2 = 2[/math], [math]x = \sqrt{2}[/math], question answered.

Now, what IS [math]\sqrt{2}[/math]? It's a number. It has the property of being irrational, which means it can't be expressed as the ratio of any two integers.

Now here's the punchline: There are more irrational numbers than rational numbers. The set of rational numbers is countably infinite, while the set of irrationals is uncountably infinite. So just on headcount alone, it's pretty dumb to deny the existence of irrationals.

Besides, [math]e[/math] is irrational, and that's a pretty damn important number that shows up all over the place. To say that it doesn't exist (in whatever sense you mean) implies that whole branches of mathematics should be discarded despite the fact that they're logically consistent and give correct answers to real-world problems.

>>14847892
>on headcount alone

>>14846721
>Feelings were hurt

>>14847892
>Depends on how retarded your definition of "is" is
It depends on how much you want to be at defining undefined. Contradiction taken to tryhard levels of autism.

>Now, what IS 2√?
Undefined

>It's a number.
Undefined

>It has the property of being irrational,
>property
Undefined

>which means it can't be expressed as the ratio of any two integers.
Which makes it "Undefined".

>Now here's the punchline: There are more irrational numbers than rational numbers
You really will never explain the universe using math.

>To say that it doesn't exist (in whatever sense you mean) implies that whole branches of mathematics should be discarded
You call it "math" yet what's being quantified isn't a number. How is that math?

>the fact that they're logically consistent
How could it be with the principles you just explained?

>>14848481
You say say "undefined" as many times as you want but it won't change the fact that [math]\sqrt{2}[/math] is in fact very well defined.

>>14839043
3 in Z_7

>>14839206
no you idiot, 1 is 1

>>14849841
>irrational is ration!
>contradicts math

Whatever, your words not mine.

>>14839043
you never took a geometry class, did you

>>14839043
OP is right and I can't IMAGINE any number that could prove him wrong.

>>14839043
[math]\begin{bmatrix}1 & 1 \\ 1 & -1\end{bmatrix}[/math]

>>14839066
>muh doodles r da sekret to da unoverz, i no da troof cuz i cownt gud