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Its kind of a bracket but I'm not sure what it means.

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I have two ideas about it: It means the number of times the expression in satisfied or it changes for $1$ or $0$ depending on the result every time the $i$ value changes.

Willie Wong
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Marx Guimarães
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  • Without context it's hard to know... A good author will have explained the notation. – Dan Rust Aug 06 '13 at 23:30
  • I think it means that its content is just a comment, and not a part of the calculation. – user1337 Aug 06 '13 at 23:31
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    My guess would be that, if $\phi$ is some statement, then $$[ \phi ] = \begin{cases} 0\ \text{if}\ \phi\ \text{is false} \ 1\ \text{if}\ \phi\ \text{is true} \end{cases}$$ But this is just a guess. More context would help. (Edited: MathJax doesn't appear to have support for the double-bar square brackets.) – Clive Newstead Aug 06 '13 at 23:31
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    Iverson bracket? – anon Aug 06 '13 at 23:31
  • @CliveNewstead Well; it does: $[\hspace{-1pt}[\mbox{Hello world}]\hspace{-1pt}]$ – Lord Soth Aug 06 '13 at 23:39
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    I think it is noteworthy that this statement in double brackets follows a period. – Karl Kroningfeld Aug 06 '13 at 23:39
  • @LordSoth: Nice work. I wish I had the patience to type that in every time instead of just \llbracket and \rrbracket! – Clive Newstead Aug 06 '13 at 23:40
  • I'll try to add some context. x and y are both arrays with same dimensions, so the statement compares if the values of x and y in the position i are the same. The H^(t-1) is there just because x is part of another array of arrays. Do this help or makes it worse? – Marx Guimarães Aug 06 '13 at 23:41
  • @CliveNewstead Haha, too bad that you can see my code, I was hoping to be more mysterious. – Lord Soth Aug 06 '13 at 23:41
  • MarxGuimaraes: Does the author give any indication of what $E^t$ is supposed to represent? In particular, does it depend on $x$ and $y$? – Karl Kroningfeld Aug 06 '13 at 23:42
  • E^t is suppose to be an error value. Its a number, in this case the result of the sum, it does depend on x and y because: x is the labels of data (like [1,2,1,2]) and y is the results of a classification on the same data (same format). – Marx Guimarães Aug 06 '13 at 23:44
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    I would go with iverson bracket then. – Karl Kroningfeld Aug 06 '13 at 23:45
  • I just searched for iverson bracket and found some info. It was hard for me to search since i didn't knew how to call this symbol and i couldn't type it because its on a pdf. Thank you so much guys. – Marx Guimarães Aug 06 '13 at 23:47
  • I'll turn my comment into an answer. – Clive Newstead Aug 06 '13 at 23:59
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    Also, when asking there you may need to provide more context: what book is it from, what area of mathematics, etc. – Alexey Romanov Aug 07 '13 at 06:28

4 Answers4

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This type of square-bracket is used in different context. One application is indeed for some sign functions.

In your example it is used identical to the so called Iverson Bracket. In this case the specific use of square brackets was advocated by Donald Knuth to avoid ambiguity in parenthesized logical expressions.

But beyond your example beware, there are other applications such as $[[z]]$ could mean round down to the greatest integer less than or equal to $z$ etc.

al-Hwarizmi
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  • Thank you I ended up finding the answer in another question (This one was created automatically). Thanks for everyone that helped – Marx Guimarães Aug 07 '13 at 15:18
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In this instance, the symbol is an Iverson bracket, defined by $$[\phi] = \begin{cases} 0 & \text{if}\ \phi\ \text{is false} \\ 1 & \text{if}\ \phi\ \text{is true} \end{cases}$$ where $\phi$ is some formula.

Willie Wong
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Clive Newstead
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This is somewhat off-topic, but might help.

Coxeter and Johnson, use square brackets to mark of a symmetry, eg [3,3] is the symmetry of {3,3}, but use double-square brackets to add a secondary extension ie [[3,3]] is the tetrahedral symmetry, along with swapping a figure and its dual. For this group, central inversion works, but for [[3,4,3]] in 4D, one needs one of Conway/Thurston's 'wanders' to move the two.

wendy.krieger
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It could very well just be a parenthetical statement (as in the English grammatical construct); e.g. that the equation to the left is true only if the condition on the right holds, or as an explanation as to why the equation is true, or maybe something else. This interpretation is encouraged by the appearance of what appears to be a period at the end of the equation on the left.

As others have said, actually showing the context would help clear things up.