Problems when calculating with a floor function

umbrella · #1 $Old$ November 3rd, 2009, 09:49 AM

Hello,

I am new here, so if I posted this in the wrong section of the forum, please forgive me and correct me when needed.

I've a small problem with using the floor function. First of all, I can't seem to be able to find a "good" definition of the floor function in mathematics. With "good" definition I mean, expressing the floor function as one function and not with "multiple functions" inside a function.

(Mostly if I know the correct definition I would rewrite the equation so I can do something with it, like when I handle something like: $|a \cdot b|$ I would rewrite it to: $\sqrt{(a \cdot b)^{2}}$

Next question is, what kind of operations can I do with a floor function? I will give some examples: $\lfloor a \cdot b \rfloor \neq \lfloor a \rfloor \cdot \lfloor b \rfloor$ , this is apparently true so I can't do this operation with a floor function. So what is possible?

This is used for answering my question: How can I simplify the following: $n_{x} \cdot a - \lfloor n_{x} \cdot a \rfloor$ ?

(if it's not possible please tell me, at this moment I do not believe it is possible because I do not know what kind of operations I can do with the floor function)

Thank you for your response and for your help!

Jameson · #2 $Old$ November 3rd, 2009, 12:51 PM

Hi, welcome to MHF.

$n_{x} \cdot a - \lfloor n_{x} \cdot a \rfloor$

Is going to leave you with just the fractional part of the product of n*a. That might have been already known to you but that's what it is. Is that all you needed, just knowing what it does?

umbrella · #3 $Old$ November 3rd, 2009, 02:00 PM

Yes, I already know what it does. However I would like to simplify it and I would like to learn more about the floor function. I would be very happy, if you can teach me some "operations" that I can do on the floor function.

Thanks for your response and help!

Jameson · #4 $Old$ November 3rd, 2009, 03:37 PM

I think the freedom with this function is limited, but here's a webpage with lots of info about it:

Wapedia - Wiki: Floor and ceiling functions

umbrella · #5 $Old$ November 3rd, 2009, 04:13 PM

Yes, I already looked at wikipedia. But I figured that since this is a math forum, this would be probably more helpfull to me than Wikipedia (because Wikipedia mostly doesn't show "tricks" and some parts of Wikipedia is just beyond my level).

But having all this, I think I can assume that there is no way I could simplify that formula. And I think I can say that there are no "operations" that works on the floor function if the numbers inside (the $\lfloor ... \rfloor$ ) aren't restricted to a subset of real numbers (oh something I forgot, and which is not equal to the set of real numbers =))

Please correct me if I'm wrong with my statements (I might have overlooked something on Wikipedia, I'm sorry for that).