# Can somebody please tell me what this means?

Does this type of bracket represent something else?

Thank you.

Note by Ruiwen Zhang
3 years, 4 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 $$x$$ ,

$$x = \lfloor x \rfloor + \{ x \}$$

- 3 years, 4 months ago