0
$\begingroup$

Let $ \mathsf{LHS} = \lfloor \lceil x \rceil \rfloor $ and $ \mathsf{RHS} = \lceil x \rceil $.

Let us call $ n = \lceil x \rceil $.

Case 1: $ n $ is even, i.e., there exists a $ k \in \mathbb{Z} $ such that $ n = 2 k $.

I’m not sure how to go on or if I’m setting this up right.

$\endgroup$
  • $\begingroup$ What is ⎤? Floor? Ceil? $\endgroup$ – Joao Nov 14 '14 at 6:59
  • $\begingroup$ You have to show that, if $n=\lceil x\rceil$, then $\lfloor n\rfloor=n$? If $n$ is the floor of some number then $n$ is its own ceiling? If $n$ is in the range of the floor function, then $n$ is a fixed point of the ceiling function? It would help a lot if I knew (a) what is the range of the floor function, and (b) what are the fixed points of the ceiling function. Beats me. You have any ideas? $\endgroup$ – bof Mar 1 '15 at 8:30
  • $\begingroup$ This question seems a bit simple and should probably be considered off topic or simple. Ceiling returns an integer. Floor only changes a number when it is not an integer. This is really a question of data types. Ceiling changes a number from R -> N. And then floor only does something when changing R -> N. It's a data type converter function. If it's the right data type then casting is literally redundant. The question is nice but I think it's one that CRUDE would say shouldn't be here, sadly. $\endgroup$ – The Great Duck Mar 4 '16 at 5:08
12
$\begingroup$

$\lceil x\rceil$ is an integer, and if $n$ is an integer then $\lfloor n\rfloor=n$.

$\endgroup$
8
$\begingroup$

First notice that $ \left \lfloor{n}\right \rfloor = n$ for all integers $ n$. And $ \lceil x \rceil $ is an integer

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.