Ceiling and Floor

**dwsmith** · November 14th 2010, 12:37 PM

$\displaystyle\left\lceil x\right\rceil=\left\lfloor x\right\rfloor +1$

Let $\displaystyle x=x'+d \ \ni \ x'\in\mathbb{Z} \ \mbox{and} \ 0<d<1$

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

How can I translate this into the RHS now?

**Plato** · November 14th 2010, 12:54 PM

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 $\displaystyle\left\lceil x\right\rceil-\left\lfloor x\right\rfloor =1$

**dwsmith** · November 14th 2010, 01:00 PM

Originally Posted by dwsmith

Let $\displaystyle x=x'+d \ \ni \ x'\in\mathbb{Z} \ \mbox{and} \ 0<d<1$

This line should let you know x isn't an integer.

**Plato** · November 14th 2010, 01:06 PM

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.

**dwsmith** · November 14th 2010, 01:14 PM

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.

**topspin1617** · November 14th 2010, 03:24 PM

Originally Posted by dwsmith

$\displaystyle\left\lceil x\right\rceil=\left\lfloor x\right\rfloor +1$

Let $\displaystyle x=x'+d \ \ni \ x'\in\mathbb{Z} \ \mbox{and} \ 0<d<1$

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

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?

**dwsmith** · November 14th 2010, 05:07 PM

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?

**roninpro** · November 14th 2010, 05:42 PM

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

**dwsmith** · November 14th 2010, 05:47 PM

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.

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