Weird brackets

Algebra Level 2

Find the number of solutions for $\lfloor x \rfloor = \{ x \}$ .

Details and Assumptions

$\lfloor x\rfloor$ denote the Floor Function .
$\{ x\}$ denote the fractional part function.

2 1 0 3 4

2 solutions

Henk Elemans
Oct 3, 2015

Assuming I understood the question correct [.] was meant to be [x] and {.} was meant to be {x} and [x] means $\lfloor x\rfloor$ and {x} means $x-\lfloor x\rfloor$ .

The integral and fractional part can never be equal unless they are both zero, so a single solution is possible.

yes you are right

Atul Shivam - 5 years, 8 months ago

Tarun Prasad Sahu
Oct 3, 2015

Fractional part will never be an integer except when there is no fractional part in a number.

In that case, fractional part is 0. Since 0 is an integer, the $only$ solution satisfying [x]={x} is x=0.

Weird brackets

2 solutions

0 pending reports