Ceiling: Difference between revisions

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{{Built-in|Ceiling|⌈}} is a [[monadic]] [[scalar function]] that gives the [[wikipedia:floor and ceiling functions|ceiling]] of a real number, that is, the least integer [[Comparison tolerance|tolerantly]] [[greater than or equal to]] the given value. This operation is also known as '''round up'''. Ceiling shares the [[glyph]] <source lang=apl inline>⌈</source> with the dyadic arithmetic function [[Maximum]]. [[Comparison_with_traditional_mathematics#Prefix|Traditional mathematics]] derives [[Ken_Iverson#Floor_and_Ceiling|its notation]] and name for ceiling from APL.
{{Built-in|Ceiling|⌈}} is a [[monadic]] [[scalar function]] that gives the [[wikipedia:floor and ceiling functions|ceiling]] of a real number, that is, the least integer [[Comparison tolerance|tolerantly]] [[greater than or equal to]] the given value. This operation is also known as '''round up'''. Ceiling shares the [[glyph]] <source lang=apl inline>⌈</syntaxhighlight> with the dyadic arithmetic function [[Maximum]]. [[Comparison_with_traditional_mathematics#Prefix|Traditional mathematics]] derives [[Ken_Iverson#Floor_and_Ceiling|its notation]] and name for ceiling from APL.


== Examples ==
== Examples ==
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       ⌈2 2.8 ¯2 ¯2.8
       ⌈2 2.8 ¯2 ¯2.8
2 3 ¯2 ¯2
2 3 ¯2 ¯2
</source>
</syntaxhighlight>


== Properties ==
== Properties ==
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       ⌈v
       ⌈v
1 1 2
1 1 2
</source>
</syntaxhighlight>


Ceiling is the dual to [[Floor]] by [[negate|negation]].
Ceiling is the dual to [[Floor]] by [[negate|negation]].
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       (⌈v)≡-⌊-v
       (⌈v)≡-⌊-v
1
1
</source>
</syntaxhighlight>


The extension for [[complex number|complex numbers]] is derived from [[complex Floor]] via this property.
The extension for [[complex number|complex numbers]] is derived from [[complex Floor]] via this property.
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       (⌈v)≡-⌊-v
       (⌈v)≡-⌊-v
1
1
</source>{{Works in|[[Dyalog APL]]}}
</syntaxhighlight>{{Works in|[[Dyalog APL]]}}


== External links ==
== External links ==

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