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Floor function identity 
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#1
Mar2213, 12:21 PM

P: 115

Hi all, I found this rather interesting formula online and I was wondering what it means. Could someone explain it to me? All help is appreciated:
http://functions.wolfram.com/Integer...or/16/03/0001/ 


#2
Mar2213, 01:23 PM

P: 2,251




#3
Mar2213, 06:03 PM

P: 115

But what does the z mod 1 mean? I've never seen people use 1 as a modular base before?



#4
Mar2313, 12:18 AM

Mentor
P: 18,345

Floor function identity
If you wish, you can put an equivalence relation ##x\sim y~\Leftrightarrow ~xy\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
Mar2813, 06:17 PM

P: 115

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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