Hey Veeky Forums, what do you prefer?

or [math]0.\overline{3}[/math]

>whereas sqrt(2) cannot.

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

done

In that case, pi isn't nonsensical either because I can express it like this: "pi."

Easy!

See

Literally nobody except for high school teachers and autistic high schoolers care about tau.

That's nonsensical though. It's like saying [math] \int \sin{x}dx = \int \sin{x}dx [/math]

Now evaluate that as a finite decimal (protip: you can't)

see

Are you trolling? That's not nonsensical, that's a valid equality.

Well no shit, the expression is necessarily infinite in 3's. Of course it's non expressable as a finite decimal.

>3i can be written down
what is the value of 3i represented as a quotient of integers?

I'm saying that you haven't evaluated anything. It's like if your professor gave you that integral and you wrote the answer was the integral. Yeah no shit, but he wants you evaluate.

Also yes, I am taking the position of the Wildberger fags who spam his shit on here.

3i/1

Fuck.
Can't have a single thread without trolls pulling out wildeburger's autistic reconstruction of mathematics. It's like rolling in shit and trying to offend people with the smell, you are still the one covered in shit.

>i is an integer

>implying it isn't
sqrt of 1 is 1 is an integer
sqrt of -1 is i is an integer in the set of complex numbers.

There's nothing to "evaluate" about sqrt(2). It's a fucking number.

Sqrt(2) is the number that when multiplied by itself gives 2. There ya go.

You just find it impossible to imagine because you are unable to understand the limitations of constantly trying to express every quantity as some quotient of whole numbers.

you are free to bait someone else now, I concede

sqrt(2) doesn't exist. There is no number which when squared equals 2. Bingo, it's not real. Is this hard for you? Really?

Sqrt(2) is not a number, it is a function evaluated at a certain input. You cannot write the output down without infinite atoms

sqrt(2)2 = 2. there is a difference between irrational and imaginary

Yeah I can, watch:
Sqrt(2)

no number except
[math]\sqrt2[/math]

Isn't 1/3 the same? 1/3 is a function. You can't write down the output in finite terms.

>captcha Decimal first

you mean sqrt(2)×sqrt(2), but yeah. just because something is irrational, doesn't mean it isn't real

>sqrt(2) doesn't exist
What is the length of a diagonal in a square of side length 1?

ITT: anons on the brick of abandoning wildeburger and concluding only natural numbers exist

1/3 is not a function it is a fraction, go back to 3rd grade

Such a square does not exist, because it's diagonal does not exist, therefore it is clear that you cannot produce a square with sides of length 1. This is proven through empirical observation.

You are using the mathematical operation of division! If you evaluate the operation you should get a result. For 1/3 that result happens to be an "infinitely" repeating decimal.

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The sides are not equal to 1, they are just close to 1. Your graphic representation is an approximation. Try again.

Riddle me this Veeky Forums:

Pythogoras theorem:

a^2 + b^2 = c^2
suppose a = b (such as in the case where a = b = 1)

then 2a^2 = c^2
by division: 2 = (c/a)^2
Therefore 2 is the square of a rational number (c/a)

But we know that there is no such rational number.

It is not division, it just happens to share the same symbol. 1/3 is a fraction. Confusingly, it looks just like 1/3 which is 1 divided by 3 which is an operation

fractions are divisions

the only way for (c/a)^2 to equal 2 is for c to equal sqrt(2), and a to equal 1. so (sqrt(2)/1)^2=(sqrt(2))^2=2. but this, we already know. thus the hypotenuse of a length-1 square is sqrt2

>Therefore 2 is the square of a rational number (c/a)
This would be true if c were a rational number.

>Therefore 2 is the square of a rational number (c/a)

No, 2 is the square of a number (c/a). You didn't show that this number is rational.

So the only way for sqrt(2) to exist if you write sqrt(2). You realize this is paradoxical right? The logical conclusion is that the number does not exist.

No, I supposed it was rational. This proves that there is no rational root of 2. Which means that the root of 2 does not exist!

you could write it as 2^(1/2) as well

If you start from wrong assumptions you'll get the wrong results. Let's assume that 1 = 0 then 2 = 1 + 1 = 0 + 0 = 0. Oh my god, 2 is equal to 0!

I just want the people ITT to admit that the only way of writing sqrt(2) is to write sqrt(2), much like sqrt(-1) can only be written sqrt(-1), or as i. In many ways Sqrt(2) is sort of "imaginary" like sqrt(-1) is, namely that we simply define a symbol to have the property that when squared it equals two. But it is not rational, nor real (it does not exist in nature).

No. Sqrt(2) exists whether i write it sqrt(2) or 1.41421... we write it sqrt(2) because it would take forever to write the full number. because its irrational. it exists like how 1/3 exists and how π exists. we cant write either of those numbers because they go on forever, so we use their unsimplified version as to keep accuracy. that is assuming you agree that 1/3 and π are real numbers. if not, go study art history

In the real, actual world, exactly 1/3 and exactly pi do not exist. If you believe otherwise then you believe that there is such a thing as a perfect circle or a perfect division of 1 into 3 equal parts. I am telling you, you cannot find a real world example of this. You can only get approximations that are close. Just like with Sqrt(2)

by that logic, negative numbers don't exist either. you can't have -2 melons. even if you owe someone 2 melons, and you don't have any. you still have zero melons

And we define the symbol 2 to have the property 2 = 1 + 1. It doesn't exist in nature either.

P implies not Q is equivalent to Q implies not P

This is called contraposition

We have these things called atoms that actually are equal though. So 1 hydrogen atom + 1 hydrogen atom = 2 hydrogen atoms. So your hypothesis that 2 does not exist in nature just fell apart.

But they're just atoms. There's not a number.

*They're not a number

I don't understand what are you even trying to do at this point. Let start from the beginning.
In you assumed that c is rational and then showed that c/a is rational. But it doesn't actually say anything about sqrt(2). Your "proof" is basically "IF sqrt(2) is rational then it's rational".

1H + 1H = 2H, sure, but the number 2 is really just abstraction. 2 is really just 2 ones. 1H + 1H = 1H + 1H. we just use the abstraction of higher numbers to make it easier on ourselves. itd be hard to say "give me 1 bushel + 1 bushel + 1 bushel + 1 bushel....." its much easier to say "give me 300 bushels" but in reality, 300 really represents 1+1+1+1....

even when your 1H + 1H ((1P+1E)+(1P+1E)) is fused together to make helium, they might be together, but fundamentally, they're still 1P + 1E + 1P + 1E. its not like they're all of a sudden one thing now. even

This is the brightest thing I heard on this thread so far.

However, there "could" be a number that when squared equals 2. Reasonably speaking, however, there likely is not one.

It was a proof that squares do not exist because their diagonals cannot exist.

didnt mean for the last "even"

It represents things that do not exist in the world. Square, rectangles and circles: all are imperfect, except in theory, but we use these perfect systems in an imperfect world.

They're for borrowing money people do not have to live above and beyond the means in which they are entitled. Negative numbers are also a way people tell other people they owe them money, or things.

>Taking the bait

Please prove that a rectangle with sides 3 and 4 doesn't exist in the world.

consider:

Suppose a and b are integers with no common factor.
2 = (a/b)^2
2b^2 = a^2
but then a is an even integer, since the squareroot of an even number is always an even number
you could write a = 2c, where c is an integer
so 2b^2 = 4c^2
b^2 = 2c^2
so b is an even integer.

But this is a contradiction of what we supposed originally, since a and b were supposed to have no common factors, but both are even and therefore share a common factor of 2.

This proves that there is no rational root of 2. Therefore the root of 2 does not exist unless we arbitarily define a "number" to have the property that when squared it equals 2. Much like we arbitrarily define the number i to have the property that when squared it equals -1. Both are nonsense. Both are essentially imaginary. Useful, sure, but imaginary.

They would be "one unit" of two hydrogen atoms.
I think atoms share electrons as they collide so it'd be impossible to ever capture and define only one hydrogen atom. Only in theory and in the moment might they be thought of as distinct.

all numbers are imaginary. your point being?

sorry, c does not necessarily have to be an integer. The proof holds regardless though.

Rationals are imaginary too.

False. Logical sense can be made of numbers like 1, 2,3, etc. without invoking the imaginary concept of infinity. Try again.

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You can't have rational fractions not equal to integers without infinitely precise division, your statement is incorrect.

Property of being imaginary has nothing to do with infinity or logical sense. I can imagine fucking dragons.

Every argument for the "realness" of Sqrt(2) ITT is readily refuted by Wildeberg in full detail and depth. Watch the fucking videos people, this is pathetic!

Neither.

1^4/3

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143x96 picture of Spider-Man? More like Ant-Man, am I right.

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.>yfw spiderman saved this thread

Here to claim back my post

that would be an irrational course of action

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I prefer the right one.

wildposting is a stale meme

What about the ratio of any square's sides to its diameter?

Tau but it will never be adopted.

>Euclid's 47th proposition is true
You are exploiting the fact that the axioms of our superior Mathematics are incompatible with yours.
That proposition applies to "triangles" having an "angle" of "pi/4" "radians".
Is it any wonder that massing together these intuitively false assumptions bearing no relation to reality
and applying the common sense of Our universe produces nonsense?
Do you really think that if "mathematicians" cared about the true Mathematics they would waste their
lives "rigorously constructing" such things as the sets of real and complex numbers -- and then double
the "dimensions" to produce such monstrosities as the quarternions, where there are at least "(5/2)""pi"
"radians" in a "circle", contradicting the earlier assumptions of the system they claim still to be working
in!

PV=nRT

This is an excellent point. Construct a square with sides of length 1. (Protip: You will never get the the sides perfectly perpendicular, as the angle would be the irrational (and thus unattainable) pi/2. Sorry guys, sqrt(2) doesn't exist, perfect squares don't exist, perfect circles don't exist, etc.

You are all working within an unrealistic number system, and thus you will be ultimately limited in the pursuit of knowledge. You must start at basic principles which make sense in the REAL world, i.e. the one we live in, not the one constructed by mathematicians to squirrel their way out of difficult problems.