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I tried to do some math in a blog post of mine and came to one with a floor function. I wasn't sure how to deal with it so I just ignored it, and then added the ceiling function in my final equation as that seemed to give me the result I wanted. I'm wondering what is the correct way of handling these functions in equations?

What I did was this:

$$\begin{align} G(n) &= \left\lfloor n\log{\varphi}-\dfrac{\log{5}}{2}\right\rfloor+1 \\\\ n\log{\varphi} &= G(n)+\dfrac{\log{5}}{2}-1 \\\\ n &= \left\lceil\dfrac{G(n)+\dfrac{\log{5}}{2}-1}{\log\varphi}\right\rceil \end{align}$$

How should I have done this in a correct way? How do I work with the ceiling and floor functions when I shuffle around with equations?

  • 3
    The floor and ceiling functions are very very deep and have very interesting connections to analytic number theory and modular forms. You might be surprised to hear this, but they are not so easy to manipulate algebraically.2010-11-05

3 Answers 3