Status Updates From Naive Set Theory

Feels good so far.
Seems like the axiom of infinity basically shows how natural numbers are generated.
Generate something from nothing, cool.
So anyway, why is it possible to generate something from nothing? Is "nothing is a thing" a prerequisite here?

Seems like we can define every common operations using inverses and composites, e.g. addition, subtraction etc.
Rules of certain operation can be defined too.
Wow, I see the whole universe.

Cool, families!

they are pretty familiar with the std::map in C++ btw, and the section introduced a lot of available operations that can be applied to such families.

Pretty intuitive. Though it took me about 1 hour to fully comprehend it.

Aber das ist Mathe, da darf ich keine Beschwerden haben haha

I've started trying to deduce this bunch of things myself yesterday. It felt and still feels perfect, comprehension has become better.
The section I've just read has introduced functions. This feels pretty functional itself lol. Haskell just hit me again.
And it finally started introducing naturals.
Yes, I know it, set theory is, in fact, able to express naturals in a fascinating way. That's pretty captivating.

Feels good.

I still don't get what a partition or something else is though.

Defining a relation as a set of ordered pairs is fascinating. I think we can basically define every binary relationship in math by doing so.

And feels like set theory is something more than just sets. Presumably, it can describe lots of concepts—naturals maybe.

Seems like set theory is more than just a theory about sets.

Yes, I know it.
Power sets don't come alone. With ordered pairs, they become useful.
Some concepts are controversial (not mathematically), but we just use them anyway.
And I've noticed that the best way to solve a problem in set theory (possibly in every type of mathematics) is to start from definitions.

Me he atrascao en la definición que hace de los pares ordenados... Creo que debería dedicarle un ratillo a leerlo tranquilamente porque es un ejercicio mental que, aunque no es especialmente útil, creo que es educativo

Combinatorics involved!
I know it, it really assumes a set, E, and does lots of operations to it.
Because due to the axiom of specification, we need a set at first to get another set.
And btw, power of sets is hard lol. It looks pretty much just like combinatorics, and I think it really is.
Anyway, it should be, given that set theory is actually part of discrete mathematics.

Axiom of unions.
Unions, intersections, disjoints, distributive laws.
Cool, so many things all at once.
But it's truly the basics. And that's mathematics.
I'm making progress, but this, indeed, consumes lots of energy.
Already overheated bro lol

Cool.
A set that contains nothing is a set.
A set that contains a set that contains nothing is a set, and it is not equivalent to a set that contains nothing.
Recursive, huh? That's the most fascinating part of set theory.
It's logical, it's interesting.
Btw, thank you Paul, your book is SOOOOO GOOOD, and it helps me a lot.

Cool. Sets are more logical than what I thought to be.

The axiom of extensionality and of specification are interesting. Axioms like the two have basically defined how sets operate.

I'm being insanely slow when reading this—and that's how mathematics works lol.

The speed is normal, but I'm going to read this tomorrow or my brain would instantly overheat lol.

Por ahora, sencillo y bonito. Además, aparecen las cosas que va diciendo el profesor de LMD en estos primeros días jajajaja