Understanding Ceil and Floor Functions

[momentum]

Its diifcult to express my question...so, i am posting this

ceil(4.5) =?
ceil(4.1)=?
ceil(4.6)=?

 

[AKG]

ceil(x) is the smallest integer which is greater than or equal to x. In particular, if x is an integer, then ceil(x) = x, and if x is not an integer, then ceil(x) > x.

 

[momentum]

ceil(4.5)=4 // is it ok ?
ceil(4.1)=4 //is it ok ?
ceil(4.6)=5 //is it ok ?

 

[Integral]

ceil(4.5)=4 // is it ok ?
ceil(4.1)=4 //is it ok ?
ceil(4.6)=5 //is it ok ?

Nope, read the definition given above, then try again.

 

[momentum]

ah...i see, all of them should be 5 ...i had confusion on fractional part .5.
but i see ..it does not care for .5 which we use for round-off.

 

[Curious3141]

Yes, all 5.

 

[momentum]

thank you for the clarifcation

 

[bomba923]

Recall that

$$\begin{gathered}<br /> \forall x \in \left( {a,a + 1} \right)\;{\text{where }}a \in \mathbb{Z}, \hfill \\<br /> {\text{floor}}\left( x \right) = \left\lfloor x \right\rfloor = a \hfill \\<br /> {\text{ceil}}\left( x \right) = \left\lceil x \right\rceil = a + 1 \hfill \\ <br /> \end{gathered}$$

$$\forall x \in \mathbb{Z},\;\left\lfloor x \right\rfloor = \left\lceil x \right\rceil = x$$

 

[jim mcnamara]

ceil -> "goes up" if it needs to, in order reach an integer
floor -> "goes down" as it needs to, in order to reach an integer
What happens with negative numbers:

$$floor( -1.1 ) = -2 \; ceil( -1.1 ) = -1$$
$$floor( -0.1 ) = -1 \; ceil( -0.1 ) = 0$$
$$floor( 0.9 ) = 0 \; ceil( 0.9 ) = 1$$