ZeroOne.ipynb

zeroone.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "ZeroOne.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "TPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/pishangujeniya/fc16d704925e11ae832e2cdb90d255c3/zeroone.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9Gah2SOsnK3F",
        "colab_type": "text"
      },
      "source": [
        "# Why $x^0 = 0$ and $0^0 = 1 ?$\n",
        "\n",
        "*Lets, find out by computing...*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RDu7rXhBnQXP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "np.set_printoptions(suppress =True,precision = 15000)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yMVFqHnt9qYd",
        "colab_type": "text"
      },
      "source": [
        "# Making decrementing list of numbers\n",
        "- Here we make a list of numbers starting from 1 and decreasing it by `stepValue` and store it in `npList`\n",
        "\n",
        "So the list will be...\n",
        "\n",
        "Suppose `stepValue` = $0.00001$\n",
        "\n",
        "if we start from number 1 then maximum count of our numbers will be \n",
        "\n",
        "> $m = 1/stepValue = 1/0.00001 = 100000$\n",
        "\n",
        "> $x_1 = 1.000000$\n",
        "\n",
        "> $x_2 = x_1 - 0.00001$\n",
        "\n",
        "> $x_3 = x_2 - 0.00001$\n",
        "\n",
        "> $x_4 = x_3 - 0.00001$\n",
        "\n",
        "> $x_5 = x_3 - 0.00001$\n",
        "\n",
        "> $\\dots$\n",
        "\n",
        "> $\\dots$\n",
        "\n",
        "\n",
        "> $x_m = x_{m-1} - 0.00001$\n",
        "\n",
        "- In such manner we are trying to go closer and closer to zero."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v488axBCnR3O",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "myNumbers = []\n",
        "prevNumber = 1\n",
        "stepValue = 0.00001\n",
        "maxNumbers = 1/stepValue\n",
        "myNumbers.append(prevNumber)\n",
        "while ((len(myNumbers) < maxNumbers) and (prevNumber > 0)):\n",
        "  currentNumber = prevNumber - stepValue\n",
        "  if (currentNumber < 0):\n",
        "    break\n",
        "  myNumbers.append(currentNumber)\n",
        "  prevNumber = currentNumber\n",
        "\n",
        "npList = np.array(myNumbers)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "prE1U5My-1lJ",
        "colab_type": "text"
      },
      "source": [
        "Printing first and last 10 numbers from our list."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wU57kiyfp4B8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 459
        },
        "outputId": "17e62491-cc0c-49b6-9623-a8f1d80df011"
      },
      "source": [
        "print(\"\\n First 10 numbers : \\n\")\n",
        "for i in range(0,10):\n",
        "  print(str(i) + \"  --->  \" + str(npList[i]))\n",
        "\n",
        "\n",
        "print(\"\\n Last 10 numbers : \\n\")\n",
        "for i in range(npList.shape[0] - 10 ,npList.shape[0]):\n",
        "  print(str(i) + \"  --->  \" + str(npList[i]))"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            " First 10 numbers : \n",
            "\n",
            "0  --->  1.0\n",
            "1  --->  0.99999\n",
            "2  --->  0.9999800000000001\n",
            "3  --->  0.9999700000000001\n",
            "4  --->  0.9999600000000002\n",
            "5  --->  0.9999500000000002\n",
            "6  --->  0.9999400000000003\n",
            "7  --->  0.9999300000000003\n",
            "8  --->  0.9999200000000004\n",
            "9  --->  0.9999100000000004\n",
            "\n",
            " Last 10 numbers : \n",
            "\n",
            "99990  --->  0.00010000000191624604\n",
            "99991  --->  9.000000191624604e-05\n",
            "99992  --->  8.000000191624604e-05\n",
            "99993  --->  7.000000191624605e-05\n",
            "99994  --->  6.0000001916246047e-05\n",
            "99995  --->  5.000000191624605e-05\n",
            "99996  --->  4.000000191624605e-05\n",
            "99997  --->  3.000000191624605e-05\n",
            "99998  --->  2.000000191624605e-05\n",
            "99999  --->  1.000000191624605e-05\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PN1uwiZL_FKh",
        "colab_type": "text"
      },
      "source": [
        "# Calculating powers\n",
        "\n",
        "Making another list of name `npPowers`\n",
        "\n",
        "> $ z = x_i | i = 0 \\to m $\n",
        "\n",
        "> $ npPowers(i,value) = (z, z^z) $"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S02-AbXIrscQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        },
        "outputId": "cf62b992-74d1-4095-948d-5a82da47c65d"
      },
      "source": [
        "npPowers = np.zeros((npList.shape[0],2))\n",
        "\n",
        "for i in range(0,npList.shape[0]):\n",
        "  npPowers[i][0] = npList[i]\n",
        "  npPowers[i][1] = np.power(npList[i],npList[i])\n",
        "\n",
        "print(\"\\n npPowers : \\n\")\n",
        "print(npPowers)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            " npPowers : \n",
            "\n",
            "[[1.                     1.                    ]\n",
            " [0.99999                0.9999900000999995    ]\n",
            " [0.9999800000000001     0.9999800003999961    ]\n",
            " ...\n",
            " [0.00003000000191624605 0.9996876193876575    ]\n",
            " [0.00002000000191624605 0.9997836278273304    ]\n",
            " [0.00001000000191624605 0.9998848773523256    ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AR-EqQY9CEKs",
        "colab_type": "text"
      },
      "source": [
        " # Plotting `npPowers` of $z \\to z^z$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "62c0wI1it1Cc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 655
        },
        "outputId": "6d777fef-6f57-44af-e5b3-fa2d0d30f53b"
      },
      "source": [
        "print(\"\\n Plotting graph...\")\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(20, 10))\n",
        "\n",
        "ax.plot(npPowers[:,0],npPowers[:,1])\n",
        "\n",
        "ax.set(xlabel='0 to 1 incrementing with stepValue', ylabel='powers of x',\n",
        "       title='Can you observe the change of power graph between 0.3 to 0.5')\n",
        "\n",
        "ax.grid()\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            " Plotting graph...\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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ukHRsZGMh1p09trtq651enrMp6CgAAAAA4tSK4gpd/tgM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\nSUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 1440x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lhnh3Hf8GtTE",
        "colab_type": "text"
      },
      "source": [
        "# Conclusion\n",
        "\n",
        "- As we move closer to $0$ from $1$ till somewhere around $0.3$ the power values presents a gradual decay; however, afterwards with the further decrement it starts increasing to reach the peak value $0.999999\\dots \\equiv 1.000$\n",
        "\n",
        "- Thus additionally, if we try for other numbers then we can also observe the behaviour of $\\frac{\\lim} {x \\to 0} x^x = 1$"
      ]
    }
  ]
}