Expert: Bobby Soltani - 8/16/2004

Question
Hello,

I was looking at a solution to a problem and saw the following result:

[2x] = [x] + [x + 1/2]
Where [x] = floor(x)

No explanation for this result was given. I tried to figure it out myself but was unable to do so. If you can explain to me how this result was obtained I'd really appreciate it. Thank you.

Answer
Hi Khan,

It is hard for me to describe the floor function without pictures so I found a website for you to look at.

http://mathworld.wolfram.com/FloorFunction.html

Basically, the trick to this problem, which you can see from the graph on the website, is that [x+1/2] = x.  Then, your equation will make sense.

Let me know if you have questions.

Bobby