Misha.P

@Silent yes, exactly

@Silent what would you say?

Hello, everyone. Looking for help, question, thanks

I'd like to show that operations on irrational numbers produce (most often) another irrational number. The approach I have in mind is to show that rational numbers make a cut $(A,B)$ and have $max(A)$ or $min(B)$, which is untrue for irrationals. And then from the bounds of these numbers reconsturct the resulting one. Is it worthwhile?

@user681391 I misread

@user681391 why is $(-1,1)\cap (1-\delta,1+\delta)=(1-\delta,1)$ and not $=(-1,1)$

Unless $\delta = 0$ which it can't be

No. $(1-\delta,1) \subset (1-\delta,1+\delta)$

It's an intersection of a point $(-1, 1)$ and range of length $> 2$

Set of all possible $\delta$s

Only if $\delta $ has an upper bond

That a neighbourhood of $1$ that doesn't intersect $(-1,1)$ surrounds a point that is outside of $(-1,1)$

So I am correct?

That would be a number outside the set

But just as any other number of that set, right?

Your definition is better

It has to be a limit point. But then again if it has to satisfy that"deleted $\delta$ neighborhood of $a$ contains points of $S$", then certainly "deleted neighborhood" implies that some point Is Not in $S$

@user681391 it is a limit point, for $\delta = 1$. However not the kind of point you asked for. Its neighbourhood will overlap with some other point in $(-1;1)$

Although, I would like to get back at my previous answer to your two examples. Perhaps there can be infinitely many neighbourhoods if we take arbitrary point of either set with arbitrary small $\delta$

@user681391 there is none

@user681391 neither of your examples has any discontinuities and therefore have no limit points.

I've seen something like that in Spivak. It's probably derrived in some way relying on the fact that $\sum_{i - odd}^{n}i=n^2$

If $B \subset A$ the $A-B$ is called complement of $B$ relative to $A$

@flowian you can go from $[1; x^2+2]$ to $[-1; x^2]$ if you account for that in $t^2$, but I don't see how that would help you in any way

I am in the process of creating a chat room

The longer answer by user10354138

@user193319 math.stackexchange.com/questions/3268706/…

Guys, what can $C(a,b)^2$ mean?

He constructed $y$ in that way based on some reasoning. I ask if anyone has any clue on what that reasoning is

Equations don't just come into existance because they will support your further hypothesis

Okay

Yes, however, I hope you understand, his elaboration on the variables doesn't justify the costruction of $y=\frac{x(x^2+3D)}{ 3x^{2}+D }$

Variables $x$ and $y$ don't appear before that in the paper. And they are introduced in these equations (marked by arrows) that are not foreshadowed themselves. I suspect they have to do with the narrowing of the bounds around $D$ but can't connect the two together. So, my question is: "Where the hell did that come from?"

It's bound by $$\lambda ^{2}< D<(\lambda+1) ^{2}$$

Number which square is to be 2 (for instance)

(the screen is from original paper)

Where the hell did that come from?

Anyone familiar with Dedekind cuts?

Hello, guys

The proof for R field in Rudin gives me chills, you must go through it

Thanks!

@CaptainAmerica16 Anderson and Feil — the one you suggested on Abstract Algebra

@CaptainAmerica16 do you perchance have a pdf?

Hope you'll enjoy them

I miss those times

god

whooo