e_limit_proof_and_visualization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f0831940",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-27T15:24:58.536596Z",
     "start_time": "2023-10-27T15:24:57.085042Z"
    }
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "from math import e\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "6274a8a5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-27T15:24:58.807970Z",
     "start_time": "2023-10-27T15:24:58.535760Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\lim_{x \\to \\infty} \\left(1 + \\frac{1}{f{\\left(x \\right)}}\\right)^{f{\\left(x \\right)}} = e$"
      ],
      "text/plain": [
       "              f(x)    \n",
       "    ⎛     1  ⎞        \n",
       "lim ⎜1 + ────⎟     = e\n",
       "x─→∞⎝    f(x)⎠        "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define a symbol of Euler's number\n",
    "Eulers = Symbol('e') \n",
    "# initialize SymPy session (configures interaction with the user)\n",
    "init_session(quiet = True)\n",
    "\n",
    "# form an equation\n",
    "expression_infinity = Eq(Limit((1 + 1 / f(x))**f(x), x, oo), Eulers)\n",
    "expression_infinity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "cc32c296",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-27T15:25:00.333552Z",
     "start_time": "2023-10-27T15:25:00.294792Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\lim_{x \\to 0^+} \\left(g{\\left(x \\right)} + 1\\right)^{\\frac{1}{g{\\left(x \\right)}}} = e$"
      ],
      "text/plain": [
       "                1      \n",
       "               ────    \n",
       "               g(x)    \n",
       " lim (g(x) + 1)     = e\n",
       "x─→0⁺                  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#form an equation\n",
    "expression_zero = Eq(\n",
    "    Limit((1 + g(x))**(1/g(x)), x, 0),\n",
    "    Eulers\n",
    ")\n",
    "\n",
    "# enable unicode characters printing (simple format, nothing technical)\n",
    "init_printing()\n",
    "expression_zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "f310e4bf",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-27T15:25:01.259425Z",
     "start_time": "2023-10-27T15:25:01.236215Z"
    }
   },
   "outputs": [],
   "source": [
    "def infinity_approaching_symbolic() -> bool:\n",
    "    \"\"\"\n",
    "    Proves the limit of the expression (1 + 1/x)^x as x approaches ∞ is equal to Euler's number 'e'.\n",
    "\n",
    "    Returns:\n",
    "        bool: True if the limit is equal to 'e', False otherwise.\n",
    "    \"\"\"\n",
    "\n",
    "    x = symbols('x')  # here, we define the variable that will be used for calculations\n",
    "    eulers_limit = Limit((1 + 1 / x) ** x, x, oo)  # define the expression, takes three parameteres:\n",
    "                                                   # Limit(expression, variable, value the limit tends to)\n",
    "    result = eulers_limit.doit().evalf()\n",
    "    # ---> doit() method automatically manipulates the expression and applies all mathematical principles needed \n",
    "    #     to perform the calculation, thus we confidentally assume that all possible inputs will be handled \n",
    "    #    correctly\n",
    "    \n",
    "    # ---> evalf() converts the symbolic value into numeric one, therefore, when the doit() has performed\n",
    "    #      its role and calculated the result (in our case for all inputs Euler's number must be obtained)\n",
    "    #      the evalf() simply converts it to the numeric value (≈ 2.718281828459045 as well-known)\n",
    "    \n",
    "    \n",
    "    # return 1) boolean value whether result (calculations performed) is equal to actual Euler's number\n",
    "    # 2) result itself (numeric value)\n",
    "    return result == e, round(result, 10)\n",
    "\n",
    "\n",
    "# as x approaches 0\n",
    "# note that zero_approaching() follows completely the same structure as infinity_approaching()\n",
    "def zero_approaching_symbolic() -> bool:\n",
    "    \"\"\"\n",
    "    Proves the limit of the expression (1 + x)^(1/x) as x approaches 0 is equal to Euler's number 'e'.\n",
    "\n",
    "    Returns:\n",
    "        bool: True if the limit is equal to 'e', False otherwise.\n",
    "    \"\"\"\n",
    "    \n",
    "    x = symbols('x')  \n",
    "    eulers_limit = Limit((1 + x) ** (1/x), x, 0) \n",
    "    result = eulers_limit.doit().evalf()\n",
    "    \n",
    "    return result == e, round(result, 10)\n",
    "\n",
    "\n",
    "\n",
    "# defined custom-exception here, nevermind, I was just testing very huge values\n",
    "class GreaterThanEulers(Exception):\n",
    "    \"\"\"\n",
    "    Custom exception class to handle values greater than Euler's number (approximately 2.71828).\n",
    "\n",
    "    This exception is raised when a value is greater than Euler's number (not the case with current distribution)\n",
    "\n",
    "    Attributes:\n",
    "        value (float): The value that triggered the exception.\n",
    "        message (str): A message describing the error, including the problematic value.\n",
    "    \"\"\"\n",
    "    def __init__(self, value):\n",
    "        self.value = value\n",
    "        self.message = f\"{value} is greater than Euler's number\"\n",
    "        super().__init__(self.message)\n",
    "        \n",
    "    \n",
    "def infinity_approaching_numeric():\n",
    "    \"\"\"\n",
    "    Shows that the limit for given values is close to Euler's number.\n",
    "\n",
    "    This function iterates through a sequence of values and calculates the limit of the\n",
    "    expression (1 + 1/value) ** value for each value. Prints the value of each calculation \n",
    "    unless the expcetion was triggered\n",
    "\n",
    "    Raises:\n",
    "        GreaterThanEulers: Custom exception raised when the limit exceeds Euler's number.\n",
    "    \"\"\"\n",
    "    \n",
    "    # generate a sequence\n",
    "    sequence = np.arange(1, 10001)\n",
    "    \n",
    "    for value in sequence:  # iterate through each value\n",
    "        # define the expression to calculate\n",
    "        expression = Limit((1 + 1 / value) ** value, value, oo)\n",
    "        # use doit() and evalf() to calculate the value\n",
    "        result = expression.doit().evalf()\n",
    "        \n",
    "        # yet in case for some values the result is bigger\n",
    "        if (result > e):\n",
    "            # therefore I decided to write a custom exception just in case\n",
    "            raise GreaterThanEulers(value)\n",
    "            \n",
    "        print(f\"For value {value} the limit is {result} (\\x1b[32mpassed\\x1b[0m)\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "fb4493da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing symbolic:\n",
      "(True, 2.7182818285)\n",
      "(True, 2.7182818285)\n"
     ]
    }
   ],
   "source": [
    "print(f\"Testing symbolic:\\n{infinity_approaching_symbolic()}\\n{zero_approaching_symbolic()}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e89121b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(f\"Testing numeric:\\n{infinity_approaching_numeric()}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "5399bc13",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-27T15:25:03.628023Z",
     "start_time": "2023-10-27T15:25:03.381560Z"
    }
   },
   "outputs": [],
   "source": [
    "# This line is typically used in Jupyter Notebook to display plots inline.\n",
    "%matplotlib inline\n",
    "\n",
    "# Define a function to plot graphs\n",
    "def graph_drive(x: np.ndarray, y: np.ndarray, label: str, color: str) -> None:\n",
    "    \"\"\"\n",
    "    Plot a graph given x and y data with a specified label and color.\n",
    "\n",
    "    Parameters:\n",
    "    - x: numpy.ndarray\n",
    "        An array of x-axis data points.\n",
    "    - y: numpy.ndarray\n",
    "        An array of y-axis data points.\n",
    "    - label: str\n",
    "        A label for the graph.\n",
    "    - color: str\n",
    "        The color of the graph line.\n",
    "\n",
    "    Returns:\n",
    "    None\n",
    "    \"\"\"\n",
    "    plt.plot(x, y, label=label, color=color)\n",
    "\n",
    "# Define a function to plot multiple graphs\n",
    "def plot_graphs() -> None:\n",
    "    \"\"\"\n",
    "    Plot multiple graphs on the same set of axes and customize the plot.\n",
    "\n",
    "    Parameters:\n",
    "    None\n",
    "\n",
    "    Returns:\n",
    "    None\n",
    "    \"\"\"\n",
    "    # Create an array of x-axis values from -10 to 10\n",
    "    x = np.arange(-10, 11)\n",
    "\n",
    "    # Define symbolic variables for equations\n",
    "    x_symbol, y_symbol = symbols('x y')\n",
    "\n",
    "    # Define data and equations for four different graphs\n",
    "    y1 = x\n",
    "    equation1 = Eq(y_symbol, x_symbol)\n",
    "    equation1 = latex(equation1, mode='inline')\n",
    "\n",
    "    y2 = -x\n",
    "    equation2 = Eq(y_symbol, -x_symbol)\n",
    "    equation2 = latex(equation2, mode='inline')\n",
    "\n",
    "    y3 = x**2\n",
    "    equation3 = Eq(y_symbol, x_symbol**2)\n",
    "    equation3 = latex(equation3, mode='inline')\n",
    "\n",
    "    y4 = -(x**3)\n",
    "    equation4 = Eq(y_symbol, -(x_symbol**3))\n",
    "    equation4 = latex(equation4, mode='inline')\n",
    "\n",
    "    # Plot each graph with a specified color and label\n",
    "    graph_drive(x, y1, equation1, color='blue')\n",
    "    graph_drive(x, y2, equation2, color='green')\n",
    "    graph_drive(x, y3, equation3, color='red')\n",
    "    graph_drive(x, y4, equation4, color='yellow')\n",
    "\n",
    "    # Add labels and a legend to the plot\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "    plt.legend()\n",
    "\n",
    "    # Adjust the y-axis and x-axis limits\n",
    "    plt.ylim(-10, 10)\n",
    "    plt.xlim(-10, 10)\n",
    "\n",
    "    # Display the plot\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "98885dd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_graphs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c0bb9923",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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