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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, 11 months ago

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1 vote

  Easy Math Editor

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*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

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  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

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[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} \( \boxed{123} \)

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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, 11 months ago

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