Why is 0.99999… = 1?
March 17th, 2009
A cool thing I learned a long time ago is that 0.99999… = 1. And I mean exactly equal. Not just “very close to”. EXACTLY equal.
Behold the proof!
Let a = 0.111111…
Then 10a = 1.11111…
10a - a = 1.11111… - 0.11111…
9a = 1.
But 9 times 0.11111… is 0.99999….
So 0.999999…. is exactly equal to 1!
This has some [...]
Finding The Square Root of i
March 11th, 2009
Some years ago, when I first learned about imaginary numbers, I asked myself the inevitable question - “What’s the square root of i?”
Okay, so i is the square root of -1. I had come to grips with that concept. But after that, when you start thinking about it… surely the square root of i must [...]
