/sci/ - Science & Math

For [math]a_{n}[/math], [math]a_{k} \in\mathbb{R}[/math] and [math]N, M[/math] counting numbers.
As definitions: [math]\sum_{n=1}^{0}a_{n}=\textit{0}[/math], [math]\sum_{n=1}^{1}a_{n}=a_{1}[/math] and
[eqn]\sum_{n=1}^{N+1}a_{n}=\left(\sum_{n=1}^{N}a_{n}\right)+a_{N+1}.[/eqn]

Also as definitions: [math]\prod_{n=1}^{0}a_{n}=\textit{1}[/math], [math]\prod_{n=1}^{1}a_{n}=a_{1}[/math] and
[eqn]\prod_{n=1}^{N+1}a_{n}=\left(\prod_{n=1}^{N}a_{n}\right)a_{N+1}.[/eqn]

As theorems:
[eqn]\sum_{n=1}^{N+M}a_{n}=\sum_{n=1}^{N}a_{n}+\sum_{n=N+1}^{N+M}a_{n}.[/eqn]

[eqn]\prod_{n=1}^{N+M}a_{n}=\left(\prod_{n=1}^{N}a_{n}\right)\left(\prod_{n=N+1}^{N+M}a_{n}\right).[/eqn]

For every [math]\sigma\in\textrm{S}_{N}[/math]:
[eqn]\sum_{n=1}^{N}a_{\sigma(n)}=\sum_{n=1}^{N}a_{n}.[/eqn].

[eqn]\prod_{n=1}^{N}a_{\sigma(n)}=\prod_{n=1}^{N}a_{n}.[/eqn].

[eqn]\left(\sum_{n=1}^{N}a_{n}\right)\left(\sum_{k=1}^{M}b_{k}\right)=\sum_{n, k}a_{n}b_{k}..[/eqn]

For [math]\textit{1}\in\mathbb{R}[/math], definition:
[math]\textit{2}=\textit{1}+\textit{1}[/math].
[math]\textit{3}=\textit{1}+\textit{1}+\textit{1}[/math].
[math]\textit{4}=\textit{1}+\textit{1}+\textit{1}+\textit{1}[/math].
et cetera.
As theorems: [math]\textit{2}+\textit{2}=\textit{4}[/math], [math]\textit{2}\times\textit{2}=\textit{4}[/math] and [math]\textit{2}a=a+a[/math]; confirming the known facts that 2+2=4 and 2*2=4.

For [math]a_{n}[/math], [math]a_{k} \in\mathbb{R}[/math] and [math]N, M[/math] counting numbers.
As definitions: [math]\sum_{n=1}^{0}a_{n}=\textit{0}[/math], [math]\sum_{n=1}^{1}a_{n}=a_{1} [/math] and

[eqn] \sum_{n=1}^{N+1}a_{n}=\left(\sum_{n=1}^{N}a_{n}\right)+a_{N+1}.[/eqn]

Also as definitions: [math]\prod_{n=1}^{0}a_{n}=\textit{1}[/math], [math]\prod_{n=1}^{1}a_{n}=a_{1} [/math] and

[eqn] \prod_{n=1}^{N+1}a_{n}=\left(\prod_{n=1}^{N}a_{n}\right)a_{N+1}.[/eqn]

As theorems:

[eqn]\sum_{n=1}^{N+M}a_{n}=\sum_{n=1}^{N}a_{n}+\sum_{n=N+1}^{N+M}a_{n}.[/eqn]

[eqn]\prod_{n=1}^{N+M}a_{n}=\left(\prod_{n=1}^{N}a_{n}\right)\left(\prod_{n=N+1}^{N+M}a_{n}\right).[/eqn]

For every [math]\sigma\in\textrm{S}_{N}[/math]:

[eqn] \sum_{n=1}^{N}a_{\sigma(n)}=\sum_{n=1}^{N}a_{n}. [/eqn].

[eqn] \prod_{n=1}^{N}a_{\sigma(n)}=\prod_{n=1}^{N}a_{n}. [/eqn].

[eqn] \left(\sum_{n=1}^{N}a_{n}\right)\left(\sum_{k=1}^{M}b_{k}\right)=\sum_{n, k}a_{n}b_{k}. [/eqn]

For every [math] \sigma\in\textrm{S}_{N} [/math]:

[eqn] \sum_{n=1}^{N}a_{\sigma(n)}=\sum_{n=1}^{N}a_{n}. [/eqn].

[eqn] \prod_{n=1}^{N}a_{\sigma(n)}=\prod_{n=1}^{N}a_{n}. [/eqn].

[eqn] \left(\sum_{n=1}^{N}a_{n}\right)\left(\sum_{k=1}^{M}b_{k}\right)=\sum_{n, k}a_{n}b_{k}. [/eqn]

For [math]\textit{1}\in\mathbb{R}[/math], definition:
[math]\textit{2}=\textit{1}+\textit{1}[/math].
[math]\textit{3}=\textit{1}+\textit{1}+\textit{1}[/math].
[math]\textit{4}=\textit{1}+\textit{1}+\textit{1}+\textit{1}[/math].
et cetera.
As theorems: [math]\textit{2}+\textit{2}=\textit{4}[/math], [math]\textit{2}\times\textit{2}=\textit{4}[/math] and [math]\textit{2}a=a+a[/math]; confirming the known facts that 2+2=4 and 2*2=4.

For [math] \textit{1}\in\mathbb{R} [/math]. As definition:
[math]\textit{2}=\textit{1}+\textit{1}[/math].
[math]\textit{3}=\textit{1}+\textit{1}+\textit{1}[/math].
[math]\textit{4}=\textit{1}+\textit{1}+\textit{1}+\textit{1}[/math].
et cetera.
As theorems: [math]\textit{2}+\textit{2}=\textit{4}[/math], [math]\textit{2}\times\textit{2}=\textit{4}[/math] and [math]\textit{2}a=a+a[/math]; confirming the known facts that 2+2=4 and 2*2=4.

noice

based thread, pity the retarded math mode is fucking you up. Next time just share screens of your pdf. I took differential geometry my last semester of college and kinda scratched the surface of general relativity.

Ok, this is how to get flawless Math Mode done:
>Open and close always: (math) and (/math), changing parentheses to square brackets.
>MathJax comands start with a backslash \ (found using [alt gr]+[[math]^{?}\prime_{\setminus}[/math]]) while using regular slash "/" like in "/epsilon" is wrong.
>NEVER finish with (\math) or (\eqn) instead of (/eqn) and (/eqn).
>Insert blank space after opening (math) or (eqn) or before closing it with (/math) or (/eqn).
>For example: (math) \example (/math) instead of (math)\example(/math) and (eqn) \sum_{\infty}^{\pi} (/eqn) and not (eqn)\example(/eqn).
>Don't press enter before or after a (eqn) ... (/eqn) block, e. g. write (math) \something (/math)(eqn) \redacted (/eqn)(math) .. (/math) and Jax will understand.
>This is the basic [math]\LaTeX[/math] guide https://sites.google.com/site/scienceandmathguide/other/-sci-infographics/joseflatex.png

>>12644027
There is your example
>([[math]^{?}\prime_{\setminus}[/math]])
>([[math] ^{?}\prime_{\setminus} [/math]])

>Nice
Nice

>>12643453
nice pic/thread

None of this applies to [math]\hat\infty[/math].

https://openstax.org

this thread is beautiful.