{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.4 + 0.2 == 0.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9007199254740992.0\n"
     ]
    }
   ],
   "source": [
    "a = 0.4\n",
    "b = 0.2\n",
    "print(1/(a+b-0.6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2/3 == 1- 1/3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.30000000000000004"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.1+0.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exemple proposé par M. Colonna, de l'Ecole Polytechnique (source : mooc Fun \"Polytechnique #Genius : promenades mathématiques\")\n",
    "\n",
    "$B = 4095.1$\n",
    "\n",
    "$A = B+1$\n",
    "\n",
    "$X_0 = 1$\n",
    "\n",
    "$X_1 = A\\times X_0 - B$\n",
    "\n",
    "$X_2 = A\\times X_1 - B$\n",
    "\n",
    "$X_3 = A\\times X_2 - B$\n",
    "\n",
    "..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X 1  =  1.0000000000004547\n",
      "X 2  =  1.0000000018631\n",
      "X 3  =  1.0000076314440776\n",
      "X 4  =  1.0312591580864137\n",
      "X 5  =  129.04063743775941\n",
      "X 6  =  524468.2550088064\n",
      "X 7  =  2148270324.241572\n"
     ]
    }
   ],
   "source": [
    "B = 4095.1\n",
    "A = B+1\n",
    "X = 1\n",
    "for i in range(7):\n",
    "    X = A*X-B\n",
    "    print('X', i+1 , ' = ', X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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