# Ceiling and Floor

• Nov 14th 2010, 01:37 PM
dwsmith
Ceiling and Floor
$\displaystyle\left\lceil x\right\rceil=\left\lfloor x\right\rfloor +1$

Let $\displaystyle x=x'+d \ \ni \ x'\in\mathbb{Z} \ \mbox{and} \ 0

$\displaystyle\left\lceil x'+d\right\rceil =x'+1$

How can I translate this into the RHS now?
• Nov 14th 2010, 01:54 PM
Plato
Quote:

Originally Posted by dwsmith
$\displaystyle\left\lceil x\right\rceil=\left\lfloor x\right\rfloor +1$

Of course that is not true if $x\in \mathbb{Z}$.

It is only true if $x\notin \mathbb{Z}$.
In which case it is well known that $\displaystyle\left\lceil x\right\rceil-\left\lfloor x\right\rfloor =1$
• Nov 14th 2010, 02:00 PM
dwsmith
Quote:

Originally Posted by dwsmith
Let $\displaystyle x=x'+d \ \ni \ x'\in\mathbb{Z} \ \mbox{and} \ 0

This line should let you know x isn't an integer.
• Nov 14th 2010, 02:06 PM
Plato
Quote:

Originally Posted by dwsmith
This line should let you know x isn't an integer.

No should not!
That line contains the word 'let'. Which is not part of the statement.
You should correctly state what you mean to begin with.
• Nov 14th 2010, 02:14 PM
dwsmith
I am absolutely content with you having others help if you are going to be so touchy and not aid in the question posed. You aren't obligated to help me. I am sure others need you.

Just to be clear by the term "you having others help" I by no means am imply for you to ask others. What I was trying to say in a nice manner was others can help me and I will be ok with it.
• Nov 14th 2010, 04:24 PM
topspin1617
Quote:

Originally Posted by dwsmith
$\displaystyle\left\lceil x\right\rceil=\left\lfloor x\right\rfloor +1$

Let $\displaystyle x=x'+d \ \ni \ x'\in\mathbb{Z} \ \mbox{and} \ 0

$\displaystyle\left\lceil x'+d\right\rceil =x'+1$

How can I translate this into the RHS now?

I don't know what you're trying to ask.

What are you trying to translate into what?
• Nov 14th 2010, 06:07 PM
dwsmith
I now have $\displaystyle \left\lceil x\right\rceil = \left\lceil x'+d\right\rceil=x'+1$

How can I make that the RHS now?
• Nov 14th 2010, 06:42 PM
roninpro
As in your other post, what is $\lfloor x\rfloor+1$? It is $\lfloor x\rfloor+1=\lfloor x'+d\rfloor +1=x'+1$.
• Nov 14th 2010, 06:47 PM
dwsmith
Quote:

Originally Posted by roninpro
As in your other post, what is $\lfloor x\rfloor+1$? It is $\lfloor x\rfloor+1=\lfloor x'+d\rfloor +1=x'+1$.

Huh?

Never mind figure it out.