What is the function [[x]]? It came from an elementary question posed in a calculus limits assignment and included this nomenclature. Thank you.
David, then I stand enlightened! I should note that either the double-bracket pair nor the single-bracket pair is particularly good notation for greatest integer, i.e., "floor", since then one must decide what notation to use for "ceiling". I believe the more usual notation is ⌊ ... ⌋ for floor and ⌈ ... ⌉ (alas, the two symbols in each of these pairs come out different sizes when I insert HTML code; LaTeX gets them right).
Yes I agree Murray! Oddly I think that the (equally awful) notation for ceiling would be ]]x[[
But so far as I'm aware, the [LeftDoubleBracket] x [RightDoubleBracket] expression has no built-in meaning in Mathematica.
Absolutely, I agree. I was just mentioning it because that symbol is listed as representing one of the notations for the greatest integer function on the page that I linked to (http://www.mathwords.com/f/floor_function.htm) as well as in the first paragraph of the wikipedia article:
https://en.wikipedia.org/wiki/Floorandceiling_functions
So I went to Mathematica and noticed that those brackets copy from mathematica to paste as ascii as [[ and ]] in a text context in other programs.
I was wondering if it was just a crude ASCII way of typing
\[LeftDoubleBracket] x \[RightDoubleBracket]
If in fact you past that into Mathematica, select it, copy it and then past it into a text editor it will appear as
[[x]]
I've never seen the double left-bracket, double right-bracket for greatest integer. Are you sure it's not [ | x | ] , that is, the greatest integer in the absolute value of x?
Mathematical notation historically has been a sort of Tower of Babel on many fronts. The nature of a system such as Mathematica is that it removes the ambiguity. But the history is fascinating nonetheless. A very interesting review was written by Stephen Wolfram a bit more than a decade ago:
http://www.stephenwolfram.com/publications/mathematical-notation-past-future/
I suspect that this is a notation for the greatest integer function (also known as the Floor function) as described here:
http://www.mathwords.com/f/floor_function.htm
Thank you! I have dabbled with greatest integer functions, least integer functions and rounding functions which all have similarly (and very inconsistently) applied markings. All are step functions and are great for challenging the kids to truly appreciate the nuances of limits. Knowing exactly what is being asked matters in evaluating this particular problem. Thanks for your help. Thought I was on the Wolfram Alpha site and see this one is different. Thanks for tolerating my intrusion on this board.
Can you give more context? Like an example or a picture showing it?
Is this introductory calculus? Or is it the kind of calculus you might have a Math Phd do?
It is very elementary calculus. "Find the limit as x approaches 3 from the left of 2[[x-3]]+4". Trying to understand the definition of the [[x]] function in order to determine the limit. Thanks for replying!
