ahafidi

$$\binom{n}{k} = \frac{n!}{k! (n-k)!}$$

$$\binom{50}{5} = 2 \space 118 \space 760 \space \space \space \& \space \space \space \binom{12}{6} = 66$$

$$\binom{50}{5} \times \binom{12}{6} = 139 \space 838 \space 160$$

ahafidi

CREATE OR REPLACE TEMP TABLE AVERAGE_RATINGS_BY_YEAR_GENRE AS
  WITH T1 AS ( -- T1 -> Common Table Expression (CTE)
    SELECT r.rating, r.year, unnest(f.genres) AS genre
    FROM Films f JOIN Ratings r ON (r.film_id = f.film_id)
  )
  SELECT year, genre, avg(rating) AS average_rating
  FROM T1
  GROUP BY year, genre
  ORDER BY year DESC, genre

ahafidi

from mistralai import Mistral

client = Mistral(api_key=MISTRAL_API_KEY)

model_instructions = "..."

# for chunk in ...
def with_synchronous_streaming(user_prompt: str):
    messages = [
        {

ahafidi

Irrationality of Square Roots of Prime Numbers

We all remember from our fundamental mathematics classes the emphasis on the irrationality of $\sqrt{2}$ using a simple proof by contradiction.

Well, it turns out that we can extend this theorem more broadly to the square roots of prime numbers with the same kind of demonstration, and that's what we're going to demonstrate here in this article. But first, let's have some reminders about what prime numbers are.

Let $p$ be a natural number, we say that $p$ is prime if and only if $p$ is different from 1 and it has only 1 and itself as divisors. Let's denote this set of prime numbers as $\mathbb{P}$.

$$\forall p \in \mathbb{N}, \ p \in \mathbb{P} \iff \begin{cases} p \neq 1 \newline \nexists(a, b) \in \mathbb{N}^2/ \ a \neq 1 \And b \neq p \ \Longrightarrow \ p = ab \end{cases}$$

ahafidi

// @lib/utils.ts

import { twMerge } from 'tailwind-merge'
import { clsx, ClassValue } from 'clsx'

export function cn(...inputs: ClassValue[]) {
  return twMerge(clsx(inputs))
}

ahafidi

const sleep = async (ms) => {
  await new Promise(resolve => {
    setTimeout(() => resolve(0), ms)
  })
}

await sleep(2000)

ahafidi

const findSmallestInterval = (numbers) => {
  numbers.sort((a, b) => a - b)
  
  let r = Number.MAX_SAFE_INTEGER
  
  numbers.forEach((e, i) => {
    if (i + 1 > numbers.length)
      return
    
    const d = Math.abs(e - numbers[i + 1])

ahafidi

const arrayCalculation = (specialArray, depth = 1) => {
  const r = []
  specialArray.forEach((e) => {
    if (Number.isInteger(e))
      r.push(e)
    
    if (Array.isArray(e))
      r.push(arrayCalculation(e, depth + 1))
  })
  return depth * r.reduce((acc, cv) => acc + cv, 0)

ahafidi

const flattenDepth = (arr, depth = 1) =>
  arr.reduce(
    (acc, cv) => [
      ...acc,
      ...(depth === 0 || !Array.isArray(cv)
        ? [cv]
        : flattenDepth(cv, depth - 1))
    ],
    []
  );

ahafidi

const zip = (...rows) =>
  rows[0].map((_, i) => rows.map((row) => row[i]))

const zip2 = (arr, ...arrs) =>
  arr.map((val, i) => arrs.reduce((acc, cv) => [...acc, cv[i]], [val]))

const zip3 = (...arrs) => {
  let r = []

  for (let i = 0; i < arrs.length; i++) {