Can somebody please tell me what this means?

Does this type of bracket represent something else?

Thank you.

#NumberTheory #Fractions

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

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 - 6 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$