A fight between the floor and the ceiling

Algebra Level 3

$\large \left\{ \left \lfloor x \right \rfloor \right\} \ \boxed{\phantom{0}} \ \left\{\left \lceil x \right \rceil \right\}$

Let $x$ be any real number . Which of the given signs should fill the box to make the equation above true?

Notations:-

$\lfloor \cdot \rfloor$ denotes the floor function .
$\lceil \cdot \rceil$ denotes the ceiling function .
$\{ \cdot \}$ denotes the fractional part function .

Cannot be determined

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1 solution

Ashish Menon
Jun 3, 2016

$\large \left \lfloor x \right \rfloor$ and $\large \left \lceil x \right \rceil$ are always integers. And fractional parts of integers is always $0$ (because $x = \left\lfloor x \right\rfloor$ for all integers).

So, $\large \left\{ \left \lfloor x \right \rfloor \right\} \color{#D61F06}{\boxed{\color{#20A900}{=}}} \left\{\left \lceil x \right \rceil \right\}$

Yeah, make sense. Nice one

How did you align the text to center ?

Jason Chrysoprase - 5 years ago

Also how to align left and right ?

Jason Chrysoprase - 5 years ago

Align left by using the $\LaTeX$ code \left and align right by using \right

Ashish Menon - 5 years ago

@Ashish Menon – Okay, thank you my friend

Jason Chrysoprase - 5 years ago

Thanks! ʕ•ٹ•ʔ. Align text by typing within $\text{\[}$ and $\text{$ }\)

Ashish Menon - 5 years ago

A fight between the floor and the ceiling

1 solution

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