Mathematics

5:12 AM

Hey I've got a question about Buddhabrots.
So wikipedia and a few other sources say that the way to calculate a Buddhabrot is to take points(c values) that aren't in the Mandlebrot set (at least up to a certain number of iterations through z^2 + c) and trace their paths to escape, since a point(c value) that escapes is by definition not in the Mandlebrot set. My question is this, how do people render Buddhabrots that show activity within the area associated with the Mandlebrot set since any value that is part of the Buddhabrot set is, again, by definition not part of the Mandlebrot set?

I'm curious because I've been trying to render a Buddhabrot from instructions on articles I find but when I try to render points that are explicitly not in the Mandlebrot set and trace their paths to escape, it produces a negative of the Mandlebrot set... which makes sense! So why do Buddhabrots produce renderings that are significantly different than the Mandlebrot set?

user400188

6:04 AM

@Michael Hardy : A small edit to your answered here: https://math.stackexchange.com/questions/148177/what-is-the-difference-between-⊢-and-⊨?rq=1
Change "proof-checking algorithm" to "provability-checking algorithm" . Since we are after an algorithm that checks the existence of a proof rather than checking whether a proof is correct or not.
Excellent answer by the way (plus easy to understand). I bookmarked it.

Abcd

6:19 AM

If A is acute, how do I find which is greater- sin A or cos A? I think it should be $sin A>=cos A$ because sin's value increases from 0 to 90 while that of cos decreases. Research effort: 2 textbooks don't have any answer. Googled too but couldn't find the answer to my question. Used calculator and found that sin 35 is less than cos 35. Can someone account for that also?

I think I should ask that on Math.SE

Leaky Nun

@Abcd below 45, cos A is greater; above 45, sin A is greater

desmos is a great tool

Abcd

@LeakyNun How?

Ok, let me check

@LeakyNun How to use it? desmos.com/calculator

Leaky Nun

desmos.com/calculator/591r27ro5h

Abcd

@LeakyNun 1 for degrees please

Is it not possible to draw a graph with values in degrees?

Leaky Nun

desmos.com/calculator/oamqpzk969

just choose degrees in settings

Abcd

6:27 AM

ok, thanks

Daminark

Hey guys

Balarka Sen

6:44 AM

hi

Araske

hello!

Daminark

Ah, you've finally rejoined us!

Araske

i exist occasionally

Daminark

Wao reax only

Balarka Sen

oh hey araske

what did i miss in the chatlog

i can't keep up with the transcript [travolta.jpg]

Daminark

6:50 AM

.jépg

Balarka Sen

JPИSKY

I am a Russian, not a French

Alessandro Codenotti

Hi chat

Secret

Interesting. For my case, the actual dream changing is not necessary obvious to me because of how time travel can appear in my dreams and thus the narrative of the dream can mask that, but something like these do happen

Yeah, I heard people said the more you participate in dream recall, the better one remembers a dream

I also heard that the style of dreaming of each individual may be unique, thus expect that your dreams might be different form everyone else

Daminark

@BalarkaSen Vodka for you, comrade

Hey @Alessandro!

Secret

I am pretty certain I found that top secret discord group, but for some reasonI cannot join

Daminark

7:05 AM

That would suggest that it's pretty top secret

Secret

Meanwhile somewhere in the other side of the world there's this massive chat group

Erdős Math Group

Hi chat

Hai @Astyx

What's up ?

7:22 AM

Hey @Astyx

Balarka Sen

@Secret It's a rather private discussion room between a few of us, sort of like the number theory room (which is gallery; nobody other than the selected few who are involved in the study group can join), except mostly not math. I very much doubt that you found it.

Daminark

@Astyx back: not too much, how about you?

Astyx

Enjoying my freedom by not doind anything

So not much either

Balarka Sen

I should be doing... Riemannian geometry!

Astyx

I should be rereading the beginning of Diff Top

Daminark

7:26 AM

re-re-ading

jfc why are you doing stuff 3 times??

Secret

Anyway, one thing that suprised me the msot is that discord is only 2 years old

I thought it has existed for some time already

Astyx

@Daminark I like to ad things

Daminark

So it seems

Secret

7:56 AM

Well, to be REALLY picky:

yesterday, by Astyx

I've never been redundant nor have I ever said the same thing twice in a row

-> Hi chat

but anyway, it is not important

Secret

9:37 AM

[Random]

It amazed me how we can have a countably infinite and mostly unique decimal expansion for any real number, but there are continuumly many real numbers

So, what about trying to extend the scope of our alphabet by having a continuum decimal expansion:

Reals:
$$s=\sum_{k=-\infty}^{\infty}\frac{a_k}{10^k}$$

??? number decimal expansion

$$s=\int_{-\infty}^{\infty}\frac{a(x)}{10^x}dx$$

Richard

@AkivaWeinberger I know that "$10=(3+i)(3-i)$, so it's a multiple of $3+i$", I did write that :) Thanks

parvin

hi ! do you guys know if this book is a good one for introduction or not?

Introduction to the theory of computation . By Michael Sipser

I checked Amazon's rating it had 4 stars :D
I'm not sure if the rating is trustworthy or not !

Secret

10:19 AM

One thing that is obvious is that the set $$\left\{s=\int_{-\infty}^{\infty}\frac{a(x)}{10^x}dx\right\} \subset \Bbb{R}^{\Bbb{R}}$$ since the latter has nonintegrable and even uncomputable functions

however the cardinality of this set is to be found out

Leaky Nun

@Secret in other words, $2^{\Bbb N} = \mathfrak c$

Secret

Did I assumed continuum hypothesis accidentally? (though I tend to assume GCH holds for most of my analysis as I am not ready to deal with cardinalities outside GCH yet)

user84215

How can I draw a diagonal arrow in a commutative diagram with AMScd in MathJax?

Secret

I have no idea. I think you need tikz for that?

user84215

What is tikz?

Hippalectryon

10:41 AM

A LaTeX package

26

A: How to draw a commutative diagram?

It is possible to do (somewhat primitive) commutative diagrams using \array: $$\begin{array}{ccccccccc} 0 & \xrightarrow{i} & A & \xrightarrow{f} & B & \xrightarrow{q} & C & \xrightarrow{d} & 0\\ \downarrow & \searrow & \downarrow & \nearrow & \downarrow & \searrow & \downarrow & \nearrow & \do...

SteamyRoot

If you want to make commutative diagrams, I can recommend TikZ + TikZ-cd

Doubt it works in MathJax, though.

user84215

What is TikZ?

SteamyRoot

It's drawing stuff in TeX

user84215

I think AMScd is better than {array} for creating commutative diagrams

Secret

[Infinite set] A naive dedekind cut arguement:

Consider the subset of the reals [0,1]

user84215

10:54 AM

Infinity is an illusion.

Secret

We can perform dedekind cuts to obtain a pair of intervals of the form [0,a],(a,1]

Now $a \in [0,1]$ and we can use the bijective map $\frac{1}{\pi} \text{arctan}(x)+\frac{1}{2}$ to show that there are continuum many elements in [0,1]

We can also pick some bijective map to show that given some a, (a,1] also has continuumly many elements. Therefore the set obtained by taking dedekind cuts over [0,1] by having $a \in [0,1]$ (i.e. the set consists of all intervals of the form (a,1], [0,a] )has in total $2^{\mathfrak{c}}$ elements.

Now, because of the way the intervals are constructed, the set $\{[0,a], a \in [0,1]\}$ is one of the two continuum sized chains ($\{(a,1],a\in [0,1]\}$ being the other)

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$Mathematics$ Mathematics