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: $\displaystyle |a \cdot b|$ I would rewrite it to: $\displaystyle \sqrt{(a \cdot b)^{2}}$

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

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

(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!