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- exhaustive abduction over formal systems (26/04/2024)
- fractal upper bound for Eis(R) the number of eisenstein integers of norm ≤ R (25/05/2020)
- riemann ζ function in ℍ (15/08/2019)
- on the collatz conjecture (09/04/2019)
- weak evidence for goldbach's conjecture (20/10/2018)
- draft on the repartition of algebraic numbers (02/07/2018)
| yet another probabilistic "paradox", as if the world needed any more (april 22nd, 2024) an algorithm wants to quantify how attractive its website is to a given user. to do so, it checks them every minute to see if they're connected, and estimates the probability of them connecting each m... |
| formalising logical invariants (february 1st, 2024) wff (well-formed formulas) are things defined via what we call a formal grammar, which defines wff kinda recursively as such:
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| that time i got chatgpt to divide by zero (january 13th, 2024) happy new year, hope y'all had nice holidays! to put an end to all this 2023 stuff, let me tell y'all about something i did around five months ago—i just didn't think it was worth a blog article bac... |
| uniform continuity on \(f:E\subseteq\mathbb R\to\mathbb R\) functions differentiable almost everywhere (december 23rd, 2023) a week or two ago, i arbitrarily fixed myself the goal of characterising uniform continuity in a more calculatory way, in order to develop a better intuition about it, and help some students get the d... |
| which numbers to test to find a primitive root ? (december 12th, 2023) finally taking time to write on there again! so, as you may know, the only values of n for which ℤ/nℤ× may be cyclic are n=2,4,pkand2pk for odd primes p and k∈ℕ (to be clear, yes, k... |
| study of an unit square-to-circle zig-zag pattern (i) (october 2nd, 2023) this is definitely going to be one in many entries about this pattern. during my research in analytic lattice group theory, i started studying this: ... |
| intuitionistic and paraconsistent logics : a semi-addendum (august 18th, 2023) it's not really an addendum, strictly speaking, since it mostly talks about more stuff than my previous post. however, what made me realise most of this is basically me realising a bunch of stuff neop... |
| motivating paraconsistent logic (pop-sci approach) (july 27th-28th, 2023) hello everypony! it's been a while because of vacations, took a bit of time for myself and all. still, i did delve into some logic-related topics, and since i've joined kane b's discord server (whose ... |
| discrete sets, sets with discrete closure, and discontinuities (june 19th, 2023) i noticed discontinuities in functions are much more well-behaved when they form discrete sets, especially sets with discrete closure. a set is called discrete if all of its elements are isolated: S i... |
| i surrender to the superiority of waterfall plots lol (june 10th, 2023) that's it, that's the post lol. basically i figured out that my skewer plots were basically like waterfall plots! well, i knew these had to exist lol, but i'm surprised it took me that long to figure ... |
| talking about function and set graphs... again (may 28th, 2023) i slightly retconned my formalisations on the drawing (≠graphs) of sets:
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| i finally understand diagonalisation lol (may 5th, 2023) i know it may sound surprising, but i'd never really understood diagonalisation until now. it seemed more like a trick than something i could really get myself, like a lot of things in linear algebra.... |
| Lp spaces measure "how close" to being integrable a function is (mostly reportative) (april 28th, 2023) integrability is usually quite close to summability. indeed, according to riemann integration, positive functions can be bounded by below and above by step/rectangular functions, with everdecreasing w... |
| when ℚ and ℝ have the same measure (april 26th, 2023) for λ the usual (lebesgue) measure, λ([0,1]∩ℚ)=0 and λ([0,1])=1. yet, any reasonable* drawing of [0,1] and [0,1]∩ℚ should look the same. there is, of course, a way to draw b... |
| visualizing infinitely dimensional spaces (april 24th, 2023) got really into hilbert spaces, fourier and all that this semester. recently, i thought of a way of representing infinitely dimensional spaces, like how we can process audio from 20 Hz to 20 kHz each ... |
| logique classique (fr*nch pdf) (april 21th, 2023) (redirect link) |
| lattice stuff (april 10th, 2023) so, i've mainly been doing a bunch of stuff with lattices from an analytical perspective recently, i've been putting everything i found worth noting in an overleaf project and i thought i'd skim over ... |
| distance of objects in pictures (march 26th, 2023) in pictures, there are vertical and horizontal field of view angles directly given by the camera. sure, most pictures we can see might be cropped, but if we know what the original FOV angle is, and an... |
| a few finite group thingies (mainly reportative, very little personal research) (march 24th, 2023) i'm more of an analyst, but i like giving algebra a go from time to time. this is one such instance. so, i was mainly thinking about finite group invariants lately, and notable elements of groups side... |
| linear interpolation, sequences, and f(1/x) = 1/f(x) : the strange case of the square root (march 21st–22nd, 2023) the usual approximation we use to compute the square root is the newton-raphson method. namely, √z is the limit of the sequence that goes an+1=(an²−z)/2an, with a0 chosen to be sufficiently cl... |
| density of αℕ fractional parts in [0,1] – a constructive approach (march 20th, 2023) when α is a rational number, αℕ can only have a fairly limited number of decimal expansions after the decimal place. for exemple, we can't converge to anything of the form n.391737636712&c ... |