What does ceil mean ?

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

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

AKG

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

Integral

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momentum said:
ceil(4.5)=4 // is it ok ?
ceil(4.1)=4 //is it ok ?
ceil(4.6)=5 //is it ok ?
Nope, read the defintion given above, then try again.
 
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

Homework Helper
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Yes, all 5.
 
thank you for the clarifcation
 
Recall that

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

[tex]\forall x \in \mathbb{Z},\;\left\lfloor x \right\rfloor = \left\lceil x \right\rceil = x [/tex]
 
Last edited:

jim mcnamara

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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:

[tex] floor( -1.1 ) = -2 \; ceil( -1.1 ) = -1 [/tex]
[tex] floor( -0.1 ) = -1 \; ceil( -0.1 ) = 0 [/tex]
[tex] floor( 0.9 ) = 0 \; ceil( 0.9 ) = 1[/tex]
 

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