Nikolaj Kuntner Nikolaj-K

This is the script for the video discussed at

https://youtu.be/7gbRTShKvp8

Cardinality individual coded reals

Z_2 reals

Constrain $d_i > 0, s_i\in{0,1}$.

$i\mapsto \tfrac{n_i}{d_i}(-1)^{s_i}$ in ${\mathbb Q}^{\mathbb N}$

Dowload the Codex UI at

https://chatgpt.com/codex/

log in with your OpenAI (I assume you're on a mac here)
create a new empty folder somewhere and then with Codex open a project/thread in there
set it to Gpt-5.3-Codex (maybe Extra High)
(during runtime you might progressively want to say Yes to various permissions - you won't go far apart from downloading python stuff if you don't have it)
start chatting with it a bit, then dump in the following longer prompt at once:

This is the script discussed in the video at

https://youtu.be/gNSv2kWRv88

Gödel arithmetization and the anti-classical Church's thesis

Outlook for this video:

On the arithmetization of proof
On Gödel incompleteness with emphasis on quantifiers
Note on Existence and Disjunction property
Note on the failure of the Least Number Principle

Video where this script is discussed: https://youtu.be/Lsf4eAGvODs

Consider a non-strictly ordered space $X$ with an (absolutely homogenous) absolute value function $|\cdot|: X\to X$ If $B:(X\times X)\to X$ is a symmetric map, then

$B(\max(x, y)-x, \max(x, y)-y) = B(0, |x-y|)$

Proof

This file starts with Exercises, which ends at exercise 10 and is followed by "Notes: Applied Optimization".

Search for "Exercise 9" for the Regression cost function minimization exercises.

Greetings Nikolaj Kuntner

Exercises - Applied Optimization

Script for the video

https://youtu.be/LfiIiSPg3Ms

$f$ ... Lebesgue-integrable over (all of) ${\mathbb R}$,

$\int_{-\infty}^\infty f\big(x + d\big),{\mathrm d}x = \int_{-\infty}^\infty f\big(x\big),{\mathrm d}x$

$\int_{-\infty}^\infty f\big(x - \dfrac{1}{x}\big),{\mathrm d}x = \int_{-\infty}^\infty f\big(x\big),{\mathrm d}x$

Probability Theory 1 – Script skeleton

2024W-Prob1__script.pdf: sections 1–5 (up to and including 5. Lebesgue-Integral)
2025W-Prob1-Collection.pdf: sections 0–3 (up to and including 3. Das Lebesgue-Integral)

Notes:

Warning: I dropped \mathcal, since it doesn't render in gist
Likewise, _\# became _H
The items have rough importance rankings
roughly "important" vs "neutral" and "random"; I'll derank a few later

The relevant content starts at page 17 in the script. The chapter ends on page 25. Note that the exercises are different ones from the listing in the script.

==== Exercise's context ====

We consider the general minimization problem $p^{\ast} := \inf_{x \in M \subseteq X} f(x),$ where $X \subseteq \mathbb{R}^n$, $f:X\to\mathbb{R}$ is continuous,

	This script is explained at

	https://youtu.be/53lvGfk9ib8


	For all $n$,
	$\int_{-\pi}^\pi\, x^{2n} \left(\dfrac{2}{1 + {\mathrm e}^{\sin(x)}}\right){\mathrm d}x = \int_{-\pi}^\pi x^{2n} \,{\mathrm d}x$

	$\dfrac{2}{1+{\mathrm e}^x} = 1 - \tanh(\frac{1}{2}x)$

	#!/usr/bin/env python3
	"""
	Minimal Wikipedia semantic search wrapper for web integration.

	Install hints (CPU):
	- python, duh
	- pip install -U sentence-transformers faiss-cpu numpy

	Expected index artifacts (see zip):
	- path/to/pages_embeddings.index (main data item, 200 MB)