I.M.Possible » Puzzle http://www.johanmk.com What is impossible with men is possible with God Sun, 07 Mar 2010 04:16:30 +0000 en hourly 1 http://wordpress.org/?v=3.0 Which one is larger? http://www.johanmk.com/2010/03/05/which-one-is-larger/ http://www.johanmk.com/2010/03/05/which-one-is-larger/#comments Fri, 05 Mar 2010 10:08:03 +0000 Johan http://www.johanmk.com/?p=200 Between these two numbers, which one is larger? 0.99999\ldots or 1?
At a quick glance, most people will say that 1 is larger than 0.99999\ldots

However, consider the following:
Let,
x=0.99999\ldots

Now,
10x = 9.99999\ldots
10x = 9 + x

By a simple algebra, we can find that
x = 1

It means that x=0.99999\ldots=1



Can anyone explain this? Does 0.99999\ldots really equal to 1?

]]> http://www.johanmk.com/2010/03/05/which-one-is-larger/feed/ 0 1=2? http://www.johanmk.com/2010/03/04/one-is-equal-to-two/ http://www.johanmk.com/2010/03/04/one-is-equal-to-two/#comments Thu, 04 Mar 2010 15:53:37 +0000 Johan http://www.johanmk.com/?p=185 I just found this old-time mathematical riddle again in some forum.

x^2 - x^2 = x^2 - x^2
x(x-x) = (x+x) (x-x)
x = x+x
1x = 2x
1 = 2

One is equal to two?! That's totally absurd.
Can you can spot the mistakes?

]]> http://www.johanmk.com/2010/03/04/one-is-equal-to-two/feed/ 4