Mathematics can be crazy at times!

One very interesting article I came across recently is the proof of the fact that 0.999.... = 1. Like most students, I immediately questioned the validity of the steps in the proof, but it turns out that this is actually true. Three proofs are shown below

Proof 1:
Let S = 0.999......
Therefore 10S = 9.999......
Subtracting the above two equations, 9S = 9.000....
Therefore S = 1

Proof 2:
We know that 1/9 = 0.111....... (by long division)
Therefore 1 = 0.999......

Proof 3: (probably the most correct one)
Let S = 0.999....
Therefore S = 0.9 + 0.09 + 0.009 + ......
The RHS of the above equation is an infinite geometric progression with first term = 0.9 and common ratio = 0.1
Therefore S = 0.9 / ( 1 - 0.1) = 1

Read all about it on http://en.wikipedia.org/wiki/0.999...

Lets Blog!

Ive always wondered what is it about blogging that attracts so many people to doing it. I figured the best way to understand it is to be part of it, so Ive decided to try my hand at blogging. Ive found blogs very useful while programming since many people write about their subtle computer programming experiences which can help immensely as opposed to going through a marathon multi-hour debugging session by only reading from a textbook.
I don't know if I'm going to get time to update the blog regularly, but lets see how it goes.