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/math/ - Mathematics

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25 Dec 2021Mathchan is launched into public
Catalog Archive

File: 3-adic integers with dual colorings.png ( 660.99 KB , 1200x1200 , 1641009124540.png )

Image
  No. 94
Reply
This board is for the discussion of mathematics.



Equations can be embedded in multiple ways: 
  • \eqn{...}
    or 
    \math{...}
    command substitutions
  • \[ ... \]
    or 
    \( ... \)
    block substitutions
  • $$ ... $$
    or 
    $ ... $
    special block substitutions
  • \begin{equation} ... \end{equation}
    or 
    \begin{math} ... \end{math}
    environments
  • by starting a line with 
    ,,
    or 
    ,eqn
    like one commonly would with >greentext.


Matrices can be embedded by using 
\begin{matrix} ... \end{matrix}
or 
\begin{array} ... \end{array}
environments in any of the above ways to embed equations, or by starting a line with 
,mat
, 
,pmat
, 
,smat
,bmat
, 
,Bmat
, 
,vmat
or 
,Vmat
and using 
&
and 
\\
symbols to delineate between columns and rows respectively.

Arrays can be embedded by using 
\begin{array}{c|c:c} ... \end{array}
environment in any of the above ways to embed equations, or by starting a line with 
,arr{c|c:c}
Post too long. Click here to view the full text.
>>
  No. 98

File: tikz-cd-doc.pdf ( 264.95 KB , 1641011017028.pdf )

Image
Mathchan supports embedding commutative diagrams:
A→aBb↓↑cC=D \qquad\begin{CD} A @>a>> B \\ @VbVV @AAcA \\ C @= D \end{CD}

This can be done by using the 
\begin{CD} ... \end{CD}
environment in any of the above ways to to embed equations, or by specifying your code after starting a line with 
,cd
.

If KaTeX's support is insufficient, diagrams can rendered using the 
\tikzcd{...}
command or by using the 
\begin{tikzcd} ... \end{tikzcd}
environment.
For example, pasting the following excerpt from the attached PDF (TikZ-CD manual): 

\begin{tikzcd}[row sep=scriptsize, column sep=scriptsize]
   & f^* E_V \arrow[dl] \arrow[rr] \arrow[dd] & & E_V \arrow[dl] \arrow[dd] \\
   f^* E \arrow[rr, crossing over] \arrow[dd] & & E \\
   & U \arrow[dl] \arrow[rr] & & V \arrow[dl] \\
   M \arrow[rr] & & N \arrow[from=uu, crossing over]\\
\end{tikzcd}

Will render as the following figure on Mathchan:



The drawback is that you will have to pause typing and wait until the diagram renders while KaTeX can be displayed instantaneously.
It is recommended that you compile any LaTeX code yourself - or in Overleaf - before attempting to paste it on Mathchan.

File: genetic.jpg ( 138.4 KB , 894x787 , 1742974452472.jpg )

Image
  No. 1120
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>>1134
I have been thinking about the concept of selfish genes, as introduced by Dawkins, over the past few days. This led me to the following consideration. From the perspective of a selfish gene, there must be an optimal degree of relatedness, right?

This idea may appear erratic. So, please let me room to explain.


Let’s consider the parent generation. Each parent has a 50% rate of passing on their genes. Basically, yes. However, there is a way for a selfish gene to further increase its chances of being passed on, namely if both parents are related and thus already share a certain percentage of genes.

So, from the perspective of a selfish gene, there must be a trade-off between the harms of inbreeding, such as the activation of harmful recessive genes or a lack of genetic diversity, and the benefits of relatedness through an increased chance of being passed on. Formally, one can write: given a certain degree of relatedness, c is the chance of harmful mutations and recessive genes, etc., while t is the chance of passing on as many selfish genes as possible.

t >> c

How you any idea how formally caculate this?
>>
  No. 1134
>>1120
There is certainly a trade off between inbreeding (bad) and relatedness (good) with respect to genetic diversity, and it is closely related to the evolution of sexual reproduction, which you also seem to have recognized. However, I'm not sure how to formalize it mathematically, but it's definitely an interesting question.

File: xiom.png ( 380.54 KB , 1080x980 , 1663002740804.png )

Image
  No. 299
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>>604 >>709 >>711 >>732 >>767 >>779 >>876 >>949 >>1081
When did you realize that the reals are fake?
Mathematics can do without infinities.
48 posts and 3 image replies omitted. Click here to view.
>>
  No. 955 >>956
In order to be mathematics, Ultrafinitist and finitists need to make a logical coherent system.
They can't. It's about the physics to deceide whether the world as a whole is infinite or finite in nature.
As far as I know, our informations doesn't allow such a inference. The topic is closed at this moment.
>>
  No. 956
>>955
I'd say finitism is moreso a philosophical perspective than anything very empirical.
>>
  No. 977
>>
  No. 1081
>>299
trve
>>
  No. 1133
I like turtles

File: asdasdas.png ( 2.99 KB , 605x152 , 1697767208017.png )

Image
  No. 512
Reply
>>532 >>535 >>539 >>548 >>713 >>744 >>1018
What I said in the subject. It's so easy to prove. Search the problem and solve it, simple as that.
17 posts and 2 image replies omitted. Click here to view.
>>
  No. 1033
jjjjjjjjjjjj
>>
  No. 1053
test post

will dedicate my time to extrapolating a curve later
>>
  No. 1054 >>1071
>>1018
>posting about iq on a mathematics board
I just want to say that i scored 110s on the mensa when i didn't know these insane fucks were doing function identities on the object numbers and 130s after finding out
iq tests are a joke on uninformed people
>but you have got to find out during the test bro
fuck off
>>
  No. 1071
>>
  No. 1132
Онлайн-слоты — это очень популярная игровых механик в сфере гемблинга.
Смысл игровых автоматов состоит в комбинациях символов, результат которых создают комбинации.
Каждый автомат имеет отличающиеся функции, разные иконки и специальные бонусы, которые добавляют азарта.
Эти игры бывают на ретро-стильные и современные, в которых встречаются разные уровни сложности.
<a href="https://raso-ug.ru">слоты это</a>
Многие игроки выбирают эти игры за интуитивность и интересный игровой процесс с минимумом тактических решений.
Современные слоты часто содержат различные специальные символы, что добавляет динамики.
В итоге, эти игры продолжают быть одним из любимых способов весело провести время в гемблинге.

File: images.jpeg ( 13.87 KB , 260x194 , 1729335144595.jpeg )

Image
  No. 1001
Reply
>>1016
I only know mathematics upto highschool only and that too barely and I want to learn mathematics from beginning rigorously. I need your help. Where should I start, where to begin. What books, what should I do and what should I not do
2 posts and 1 image reply omitted. Click here to view.
>>
  No. 1124 >>1125 >>1126
>1001
this altchan is dead
every board.
>>
  No. 1125 >>1126
>>1124
Not completely dead, but pretty dead. In a way it's not really been much alive yet, still in the womb.
>>
  No. 1126 >>1127
>>1124
>>1125
The idea behind it is very good. Yet, it lacks of a community. Since you can get really math-help in other communities around the web, there is not much room left for a chan like mathchan.
>>
  No. 1127
>>
  No. 1128
testing captcha don't mind me

File: IMG_20220714_001733.jpg ( 5.31 KB , 240x60 , 1657768669674.jpg )

Image
  No. 236
Reply
>>237 >>239 >>242 >>247 >>837
-1/12

contradiction or too complex for mere mortals to understand?
9 posts and 2 image replies omitted. Click here to view.
>>
  No. 305
Behold, the Barnett-Tooker-Wildberger conjecture.

Let

ζ^b(s)=∑k=1∞^−bn−s\qquad \hat\zeta_b(s) = \sum_{k=1}^{\hat\infty - b} n^{-s}


then

ζ^e+π+2(−1)=eiπ11+0.999…\qquad \hat\zeta_{e + \pi + \sqrt 2}(-1) = \frac{e^{i\pi}}{11 + 0.999\dots}
>>
  No. 315
I still don't get it.
>>
  No. 811
Contraddiction, because in Ramanujan's proof there are mistakes i.e. the term equals zero changes the number of step in the serie and also it's true that
2>Σn=0+∞12n 2 > \Sigma_{n=0}^{+\infty} \frac{1}{2}^n
>>
  No. 837
>>236
it diverges up, right?
and the limit is the first value something dosent reach
therefore, the limit of the series must be down
>>
  No. 1122

File: 1705233653759.png ( 201.38 KB , 1139x804 , 1713480390587.png )

Image
  No. 724
Reply
>>727 >>731 >>940
If you had a math exam and you could use your phone with internet while attempting the paper, what service would you use to solve questions?
Topics:
-Propositional Calculus
-Methods of Proof
-Boolean Algebra and Circuits
-Sets, Relations and Functions
-Combinatorics
-Some more Counting Principles
-Partitions and Distributions
16 posts and 1 image reply omitted. Click here to view.
>>
  No. 791
>>754
Mobilism
>>
  No. 940
>>724
fart
>>
  No. 1019
what i say, fuck niggers
>>
  No. 1038 >>1118
Surely the answer has to be Wolfram Cloud. Mathematica + WA at your fingertips
>>
  No. 1118
>>1038
Do it manually

File: Rational-and-Irrational-Numbers-768x678.jpg ( 56.32 KB , 768x678 , 1738595323081.jpg )

Image
  No. 1080
Reply
>>1089
So what are the real numbers that neither rational or irrational.
>>
  No. 1089
>>1080
That subset is empty and the diagram doesn't say otherwise
>>
  No. 1110
The diagram clearly says that there are real numbers in between. My brother found one the other day. It is called t, t is neither rational or irrational

  No. 136
Reply
>>137 >>173 >>667 >>371 >>372 >>403 >>414 >>448 >>474 >>550
Is thrembo real? It's an integer between 6 and 7.
46 posts and 6 image replies omitted. Click here to view.
>>
  No. 833 >>838
>>832
The final answer is 3 and in >>830 it is 2.
>>
  No. 838
>>833
no the answer is clearly 2
two integers cant represent a complex number
>>
  No. 839
sneed
>>
  No. 962
logsday is the thremboth day of the week
>>
  No. 1106

File: 1725321685516r.png ( 28.95 KB , 1500x1500 , 1740952559180.png )

Image
  No. 1099
Reply
>>1100
It is both kinda surprising and disappointing that the easiest way to compute the derivative of
arc sinarc\ sin
is to solve the integral of
1−x2\sqrt{1-x^2}
geometrically.

Just by looking on a quarter of a circle with angle in it you know that:
∫1−x2dx=arc sinx2+x1−x22\int{\sqrt{1-x^2}}dx = \frac{arc\ sinx}{2} + \frac{x\sqrt{1-x^2}}{2}


By deriving everything we get:
1−x2=(arc sinx)′2+(x1−x2)′2\sqrt{1-x^2} = \frac{(arc\ sinx)'}{2} + \frac{(x\sqrt{1-x^2})'}{2}


And now it's easy to get
(arc sinx)′(arc\ sinx)'
out of the equation and solve it.

It is
11−x2\frac{1}{\sqrt{1-x^2}}
if anyone asked.

Then you can compute
(arc cosx)′(arc\ cosx)'
:

(arc cosx)′=(arc sin(1−x))′=(arc\ cosx)' = (arc\ sin(1-x))' =

=(1−x)′11−(1−x)2=...= (1-x)'\frac{1}{\sqrt{1-(1-x)^2}} = ...


Similarily and even easier
(arc tanx)′(arc\ tanx)'
because it's just a derivative of a fraction of functions.
>>
  No. 1100 >>1102

File: Ears.gif ( 357.71 KB , 425x599 , 1740956279555.gif )

Image
>>1099

the inverse function of any differentiable bijection can have
its derivative computed via the chain rule. just differentiate their composition.

gross wojack picture btw
>>
  No. 1102
>>1100
Yes, now I see. I suspected that there should be some easier way to do this because these are inverse functions.

This wojack is a homage to some Serbian who was shilling Lukyon on the soy wojak forum. He also used this "neutral feraljak".

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