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Can somebody please tell me what this means?

Does this type of bracket represent something else?

Thank you.

Note by Ruiwen Zhang
2 years, 3 months ago

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It's not the Bracket, it's the Floor function. It means the greatest integer less than or equal to the number inside, or simply the integer part of a number.

e.g. \(\lfloor 3.56 \rfloor = 3 , \lfloor \pi \rfloor =3 , \lfloor -2.34 \rfloor = -3\)


There's one more of this kind, the Ceiling function. \(\lceil x \rceil\)

It is the Smallest integer greater than or equal to \(x\).

e.g \( \lceil 3.45 \rceil = 4 , \lceil -2.34 \rceil = -2 , \lceil \pi \rceil = 4\)


Also, the fractional part of a number is denoted by \(\{x\}\) and \( 0 \leq \{ x \} < 1\) always.

e.g \( \{ 3.67 \} = 0.67 , \{1.234\} = 0.234 , \{ -2.45 \} = 0.55 \)


If you're surprised at \(\{ -2.45 \} = 0.55\) ,

\(\bullet\) \(-2.45 = -3 + 0.55 \implies \lfloor -2.45 \rfloor = -3 \text{ and } \{-2.45\}=0.55\)


Hence you can write for every real number \(x\) ,

\(x = \lfloor x \rfloor + \{ x \} \) Aditya Raut · 2 years, 3 months ago

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