/sci/ - Science & Math

>>12242859
>How do you not pay for phd
They pay me for doing it.
>Are you euro (peeing)
Yes.

>>12242876
False.

hi friends whats happening today? pls not more gay satellites?

>>9507950
>I was asking for mathematical notation.
[math]\varphi\colon[0, 2]\to\mathbb{R}[/math]

>>8959671
It is good for people who do stuff somewhat related to logic. If you are a logician, you will find some chapters interesting. If you are a computer scientist, you will be happy to see him talk about lambda calculus. If you are a topologist, you will be happy to notice he talks about the Stone duality, and then you can apply the Boolean stuff he talks about (this -> https://en.wikipedia.org/wiki/Stone_space <- this). But, if you are not into (topo)logic(al things), then maybe some other book.

First: for any integers {math]m. n[/math] their difference is either 0 or {math]|m-n| \ge 1[/math]. Since the sequence converges to some [math]a \in \mathbb{Z}[/math], for every [math]\varepsilon > 0[/math], there is an integer [math]N>0[/math] such that [math]|a_n - a|<\varepsilon[/math], for all [math]n>N[/math]. Choosing [math]\varepsilon = \frac{1}{2}[/math], one obtains an [math]N[/math] such that [math]|a_n - a|<\frac{1}{2} \Leftrightarrow |a_n-a|=0 \Leftrightarrow a_n=a[/math] for all [math]n > N[/math].

>>8734395
Take any topological space [math]X[/math], sober or not. You then have have the lattice [math]\Omega (X)[/math] of open subsets, giving you the frame of the space. Then, the locale [math]L(X)[/math] is the corresponding object in the category of locales, or the dual category of frames, and you now have a functor [math]L \colon \textbf{Top} \to \textbf{Loc}[/math]. For any locale, one can define a spectrum by considering its set of all completely prime filters, and equiping this with a suitable topology. Now, this gives rise to a functor [math]S \colon \textbf{Loc} \to \textbf{Top}[/math], and all the spectra themselves are sober spaces, so now the composite of these functors defines a sobrification [math]X \mapsto SL(X)[/math].

>the guy steals $100
-$100
>he pays for stuff worth $70 with the bill
-$70
>he gets $30 in change
-$30

Total: $200. Trust me, I'm an algebraic topologist.