Floor function identity

  1. jcsd
  2. the [itex]\theta[/itex] function is the unit step function, so they are creating a staircase function out of the steps (the infinite summation), and that becomes the floor function.
     
  3. But what does the z mod 1 mean? I've never seen people use 1 as a modular base before?
     
  4. micromass

    micromass 19,230
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    The notation ##z## mod 1 means that you take the element ##x\in [0,1)## such that ##z-x\in \mathbb{Z}##.

    If you wish, you can put an equivalence relation ##x\sim y~\Leftrightarrow ~x-y\in \mathbb{Z}## on ##\mathbb{R}##. We can then look at equivalence classes. It won't be the exact same thing as what I said in my first sentence though.
     
  5. Are there any formulas that compare any positive real number r with floor[r]? I know that their difference is the fractional part of r, which is {r}, but I mean are there any formulas where you can obtain these values systematically?
     
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