Here’s a basic computer program for the politicians of today, expressed in different computer languages:
C Language
#include <stdio.h>
int main(){ printf(”Hello, Garci!n”);
return 0;}
C++
#include <iostream>
using namespace std;
int main(){ cout << “Hello, Garci!” << endl;
return 0;}
C#
public class WireTapGate{ public static void Main() { System.Console.WriteLine(”Hello, Garci!”); }}
Pascal
program WireTapGate; begin writeln(’Hello, Garci!’);end.
Java
import java.awt.*;
public class WireTapGate{ public static void main(String[] args) { System.out.println(”Hello, Garci!”); }}
Perl
#!/usr/bin/perl
use strict;use warnings;
my %hash = (wiretapgate => ‘Hello, Garci!’);
my $stmt = $hash{wiretapgate};print “$stmtn”;
Visual Basic
Option Explicit
Public Sub Form1_Load()
MsgBox “Hello, Garci!”
End Sub
Visual Basic .NET
Imports System Module WireTapGate Sub Main() Console.WriteLine(”Hello, Garci!”) End SubEnd Module
ASP
<% Response.Write “Hello, Garci!<br />”%>
PHP
<?php echo “Hello, Garci!<br />”;?>
SQL
SELECT 'Hello, Garci!' AS WireTapGate;
JavaScript
<script type="text/javascript"><!– var wireTapGate = “Hello, Garci!”;
alert(wireTapGate);//–></script>
Windows API
#include <windows.h>
int WINAPI WinMain(HINSTANCE, HINSTANCE, LPSTR, int){ MessageBox(NULL, “Hello, Garci!”, “Message”, MB_OK); return 0;}
*nix Shell Script
#!/bin/sh WIRETAPGATE=”Hello, Garci!” echo $WIRETAPGATE
x86 Assembler
.model small.stack.datamessage db “Hello, Garci!”, 0Dh, 0Ah, “$” .code main proc mov ax,seg message mov ds,ax mov ah,09 lea dx,message int 21h mov ax,4c00h int 21hmain endpend main
Markup Languages
HTML
<html> <head>
<title>Wiretapgate</title> </head> <body> Hello, Garci! </body></html>
XML
<?xml version="1.0"?><WireTapGate> <Statement>Hello, Garci!</Statement></WireTapGate>
I Know
Yasmien Kurdi
Sweet 18 theme song
I don’t need to own a fancy car
To drive with you around the city
I don’t need to live in a palace like house
A simple home is enough for me
I don’t need much
Only your attention
I had to hope
To make me feel that i am not alone
I know
Is you my life is worth living
I know
Is you my life is gonna be just fine
I know
If you each day begins with a smile
I don’t really have to worry
Somethings won’t workout for me
I don’t really have to bother
Just as long as you here with me
I don’t need much
Only your affection
To see me through
To make me feel that i am not alone
I know
Together we can make our dreams come true
I know
But through the years we won’t be growing old
I know
Counting stars won’t be so hard to do
There will be your always time
At the end of the tumble shine
Our love for each other never fails
Baby i just know
(i know)
I know
(i know)
I know… wooahh..
I know
(i know)
I know
(i know)
Wooahh…
I don’t need much
Only your affection
To see me through
To make me feel that i am not alone
One reason why Dr. Edgar Escultura sought to trash the trichotomy axiom is because of an apparent paradox that 0.999… = 1. But 0.999… = 1 is already proven true in mathematics.
However, I agree that the equation 0.999… = 1 is not intuitive, because in the real world we know that 0.999 is less than 1.
But take note that although 0.999 is less than 1, 0.999… (with the three trailing dots) is not. Pay attention to the three dots.
The three dots in 0.999… means that the decimal point is followed by an infinite number of 9’s. In the same manner, 0.333… means a number with an infinite number of 3’s trailing its decimal point.
These nonterminating repeating decimals sometimes arise when dividing two counting numbers. Say, the fraction 1/3. If we want to obtain the decimal representation of 1/3, we simply divide 1 by 3. Using the manual division we learned in school, 1 divided by 3 is represented as
+—— 3 | 1
Since 1 is smaller than 3, we need to append a decimal point and a zero to 1, making the division look like this:
+—— 3 | 1.0
Now we can divide by treating “1.0″ as “10″:
.3
+——
3 | 1.0
- 9
——
1
The division leaves a remainder of 1. We can still continue to divide by appending another zero to “1.0″ and “bringing down” the zero to the remainder. The result is this:
.3
+——
3 | 1.00
- 9
——
10
Treating the remainder as “10″, we can divide it by 3 :
.33
+——
3 | 1.00
- 9
——
10
- 9
——
1
The remainder is again 1. We can still append zeroes and obtain the following:
.333
+——–
3 | 1.000
- 9
——
10
- 9
——-
10
- 9
——-
1
This again leaves a remainder of 1, so the process would continue indefinitely, in fact infinitely. So we can say that the decimal representation of 1/3 is 0.333… (with the three dots). Through this process, we can also deduce that 1/9 is 0.111… and 8/9 is 0.888… .
Now let’s proceed to the proof that 0.999… = 1. There are many ways to prove it, but I’ll show you two ways.