This question of mine is a soft question. In this question I would like to ask
Is there a General formula for $\lfloor a+b\rfloor$?
In this question both $a,b \in \Bbb Z$ and $\lfloor \quad \rfloor$ is the floor function. I tried searching online for this but found none. Any help/hint is appreciated
Thanks in advance 🙂
Edit : Can $\lfloor a+b \rfloor = \lfloor a\rfloor + \lfloor a + b -\lfloor a\rfloor \rfloor$?
I tried to prove it in this way.
We know that $$\lfloor x+n\rfloor = \lfloor x\rfloor + n$$
if $n\in \Bbb Z$
So, $$\lfloor a \rfloor + \lfloor a+b-\lfloor a\rfloor \rfloor = \lfloor a \rfloor + \lfloor a+b\rfloor – \lfloor a \rfloor = \lfloor a+b\rfloor$$
Is this correct?
Best Answer
The floor function restricted to $\mathbb Z$ is the identity function. So you can simply skip it! It ain't don't doing nothing!