That is the version for retards.

>>107786343
okay well we are going to need to get into inception level of retardation then. like putting a model school bus inside a short bus.

>>107786259
Russell:
>I can create whole math from pure logic; none of that a priori knowledge shit
"really? define number 2"
> {{}, {{}}}

>>107786259
>how is x a function on itself and then another function yielding a domain is applied to it again.
In (n f x), think of x as the "zero" value, and f as the "increment" operator. Except that instead of hard-coding those two in the definition of n, we make them arguments so that you can do other operations (like addition, multiplication, etc.)
>But that's not what numbers are!
Well think very carefully what are numbers really? What is their essential number-ness all about? It's very hard to put your finger on!
The definition given actually works. Really. It's not the only possible one.

>>107786932
think very carefully if your schizo talk makes any sense to anybody who doesn't already understand numbers.
> you see it's really simple
> 2 is just "eff eff"
> 3 is just "eff eff eff"
> and "eff" is just... so let me introduce the Zermelo-Fraenkel framework

>>107786259
f->(x->x)
f->(x->f) x
f->(x->f) (f x)

You give 0 a function.
add_12()
It takes add_12() and returns
(x->x)
you give it x=5 (or lf.lx.f^5 x)
it returns 5 (or lf.lx.f^5 x)

You give 1 a functon.
add_12()
it takes add_12() and returns
(x->add_12()) x
you give it x=5 it returns
add_12(5)
17

The numbers are just labels. They only refer to how many times a function was applied. But they do act like

>>107786259
There is no use-case for lambdas. Learning lambda calculus / haskell (you're probably learning lambdas for haskell) is an unemployment endeavor .

>>107786259
Think about it like this, you see the λ? Imagine you start and the top of the lambda and you come down to where it splits, it's a branching path. If you stay there and don't make a decision, you're at 0. If you choose a path, you would made a decision once. Now you drop down to the next lamba on the list. If you stay there, you stay at 1. If you choose a path, you will have chosen yet another path incrementing how many decision you've made by 1. Every time you choose a path, you increment the amount of decisions you have made. By making decisions and keeping track of how many decisions you've made, you can count.

>>107786259
THIS IMAGE MAKES NO SENSE.

WTF IS "X" THEN?

>>107786259
because you can pass function as x

>>107786927
Those were created by von neumman though

Maybe this will help
https://tomstu.art/programming-with-nothing

>>107786259
n is how many times the function is applied to x. If f is applied 0 times, x is the output. If f is applied 1 time, f x is the value of produced. If f is applied 2 times, f (f x). Church numerals just encode repetition.

>>107787420
x is a variable, could be anything, it's "not your problem". it's a box.

Imagine you're an assembly line worker. Boxes come in one line, your job is to pick them up and push them out on the other line. What's in the Boxes? Who gives a shit, do your job.

job: (box) -> (box)
this is your job description: you take a box, you output a box. This is the "identity job".
λ(box).(box)
still the same description, just some fewer symbols
but, says the (asshole) mathematician, I can describe it with even fewer symbols! (idk why, probably had to pay for every letter or something)
λx.x
Ah, there we go
still your same (shitty) job description, still the same job.
You take in the box, you put out the box.
Listen to some podcasts in the meanwhile.

>>107787420
The image is just recursion without a base case.
In practice, you'd have a predicate which passes either f or a base case to f(x). If it passes f, then that's simply more recursion. Otherwise, the recursion stops.