Sqrt(2) doesn't exist

There is no answer to sqrt 2 prove me wrong.

how can I prove you wrong when you're right?

The number is very well defined, but it has infinite decimal places in any integer base, so you'll either have to write sqrt(2) or write an equation that will reach the number after infinite steps.
Basically, approximations are more than good enough.

dude forget the dumbass topic why are you using a picture of an ape?

>real number
>infinite decimal places

[math]1.0^2 = 1.00[/math]
[math]1.1^2 = 1.21[/math]
[math]1.2^2 = 1.44[/math]
[math]1.3^2 = 1.69[/math]
[math]1.4^2 = 1.96[/math]
[math]1.5^2 = 2.25[/math]
[math]1.6^2 = 2.56[/math]
[math]1.7^2 = 2.89[/math]
[math]1.8^2 = 3.24[/math]
[math]1.9^2 = 3.61[/math]
[math]2.0^2 = 4.00[/math]

Oh would you look at that! x^2 crosses 2 between 1.4 and 1.5
Looks like it does exist!

> IVT

Wrong. There is no point on a number line that is sqrt(2).

Wrong. There is definitely a point, and it's between 1.4 and 1.5 unless the function [math]x^2[/math] makes weird jumps and dips, which it doesn't.

Wrong. There are no jumps and dips because sqrt2 is a finite point and it doesnt exist.

1 doesn't exist. Prove me wrong.

Are you some sort of rationalist? Do you dislike numbers you can't write as fractions? Does it rustle your jimmies?

there's no point for any number on a numberline unless you mark it there.

Pythagoras says hi

How long is the diagonal of a square with side length 1?

an imaginary number called sqrt2. However it's not a real number.

you're playing with words here

any rational has a point on a number line.

>real numbers
Wildburger would like to interject.

Any irrational has a point on a number line.

Are you implying the square root of 2 is on the imaginary number line? Wrong. Any imaginary number [math]x*i[/math] when squared becomes a negative number.
[math]x\cdoti=-x^2[/math]

Waste of trips.

Quadrature of 2.
> forcing your linear metric this hard

You're just parroting what other people have said. There's no solution for sqrt2, hence it's not a real number.