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I am curious to know what type but I know that one is greatest integer parent function. There is another one that explains it and I want to know what another function represents that?

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Double square brackets $[\![a, b]\!]$ are used also to mean the interval of all integers between a and b included.

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I feel that your answer is here : https://in.answers.yahoo.com/question/index?qid=20090710203054AA3mCg9 Here, it is said that the double brackets ($[[x]]$) mean rounding off, to be frank.

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