1. ## floor function question

I have never dealt with floor functions before, and I had trouble understanding the proof in my textbook.
Here's the portion of the proof:

$\frac{1}{2}\sum_{L=1}^{v}\left \lfloor \left ( \frac{v-1}{2} \right )^2 \right \rfloor\leq \frac{v}{2}\left \lfloor \left ( \frac{v-1}{2} \right ) \right \rfloor$

Also, is there some online material where I could study about floor/ceiling functions?

2. ## Re: floor function question

Hey Yuuki.

Are you supposed to have an L inside there somewhere (instead of a v)?

3. ## Re: floor function question

Originally Posted by Yuuki
I have never dealt with floor functions before, and I had trouble understanding the proof in my textbook.
Here's the portion of the proof:

$\frac{1}{2}\sum_{L=1}^{v}\left \lfloor \left ( \frac{v-1}{2} \right )^2 \right \rfloor\leq \frac{v}{2}\left \lfloor \left ( \frac{v-1}{2} \right ) \right \rfloor$

Also, is there some online material where I could study about floor/ceiling functions?
Here is a good summery of the properties of the floor function.

But there is a typo in the OP, a missing L.

4. ## Re: floor function question

Thanks for the replies.
As for the typo, I don't know how it's supposed to be, because that was what it said in the textbook.
Would it make sense if you replaced the v under summation with L?

5. ## Re: floor function question

Hi,
I guessed what the supposed inequality is, but this guess is a false inequality. I've attached some remarks on the floor function and a similar inequality that is true. I think it's worth your while to read at least the easy facts about floor.

6. ## Re: floor function question

Wow, thank you very much for the two informative sheets!
It helped that the facts came with proof.
I think I was able to become a bit more familiar with the floor function and I managed to follow through your last proof.