I'm reading a 1975 paper by a Polish mathematician (Michal Misiurewicz) written in English and published in Astérisque. It uses some notation that I'm not familiar with, although I can understand it from the context. It seems he's using the notation $E(x)$ to represent the floor function, $\lfloor x\rfloor$. Is this usage well known? (it occurs to me that E is the first letter of entier, the French word for integer).

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    $\begingroup$ I have seen this notation only used for expectation of a random variable. $\endgroup$ – user661541 Aug 16 '19 at 19:52

Although I have never seen such usage of this notation it is worth noting the following quote from the Wikipedia page on this topic:

"The notion of the integral part or integer part of $x$ was first introduced by Adrien-Marie Legendre under the name entier (French for "integer") in 1798, when he needed the concept for his proof of the Legendre's formula."

Thus it would make sense to shorten such an "entier" function to simply $E(x)$.

Edit: In some European countries the modern name for the floor function is the "entier" function (see this Dutch Wikipedia article). This may be the case in Poland.

  • $\begingroup$ Thanks for this. I guess it might have been a good idea for me to look at wiki. $\endgroup$ – anthonyquas Aug 16 '19 at 20:05
  • $\begingroup$ So I have now confirmed with a Polish mathematician friend that the floor function is indeed called the entier function in Polish. He recalled having seen the $E(x)$ notation. $\endgroup$ – anthonyquas Aug 16 '19 at 22:24
  • $\begingroup$ This is a nifty bit of history / linguistics of which I was previously unaware. It amuses me that integer can start with any of "I", "E", or "Z" in modern mathematics. ;) Thank you, Peter Foreman. (+1) $\endgroup$ – Xander Henderson Aug 16 '19 at 22:57

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