Greater than: Difference between revisions

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{{Main|Comparison function}}
{{Main|Comparison function}}


{{Built-in|Greater than|<nowiki>></nowiki>}} is a [[comparison function]] which tests whether the left [[argument]] is [[Tolerant comparison|tolerantly]] greater than and not equal to the right argument, returning 1 if this is the case and 0 otherwise. It is the [[Not|negation]] of [[Less than or Equal to]] (<source lang=apl inline>≤</source>).
{{Built-in|Greater than|<nowiki>></nowiki>}} is a [[comparison function]] which tests whether the left [[argument]] is [[Tolerant comparison|tolerantly]] greater than and not equal to the right argument, returning 1 if this is the case and 0 otherwise. It is the [[Not|negation]] of [[Less than or Equal to]] (<syntaxhighlight lang=apl inline>≤</syntaxhighlight>).


== Boolean function ==
== Boolean function ==
{{Main|Boolean function}}
When the arguments to Greater than are [[Boolean]], it is the [[wikipedia:material nonimplication|material nonimplication]] [[Boolean function]], also known as the [[wikipedia:NIMPLY gate|NIMPLY gate]]:
When the arguments to Greater than are [[Boolean]], it is the [[wikipedia:material nonimplication|material nonimplication]] function, also known as the [[wikipedia:NIMPLY gate|NIMPLY gate]]:
::{|class=wikitable
{|class=wikitable
!<syntaxhighlight lang=apl inline>></syntaxhighlight>!!<syntaxhighlight lang=apl inline>0</syntaxhighlight>!!<syntaxhighlight lang=apl inline>1</syntaxhighlight>
!<source lang=apl inline>></source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source>
|-
|-
!<source lang=apl inline>0</source>
!<syntaxhighlight lang=apl inline>0</syntaxhighlight>
|<source lang=apl inline>0</source>||<source lang=apl inline>0</source>
|<syntaxhighlight lang=apl inline>0</syntaxhighlight>||<syntaxhighlight lang=apl inline>0</syntaxhighlight>
|-
|-
!<source lang=apl inline>1</source>
!<syntaxhighlight lang=apl inline>1</syntaxhighlight>
|<source lang=apl inline>1</source>||<source lang=apl inline>0</source>
|<syntaxhighlight lang=apl inline>1</syntaxhighlight>||<syntaxhighlight lang=apl inline>0</syntaxhighlight>
|}
|}
In the context of logic, it can be read as ''but not''.
In the context of logic, it can be read as ''but not''.
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=== Documentation ===
=== Documentation ===


* [http://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Greater.htm Dyalog]
* [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Greater.htm Dyalog]
* [http://microapl.com/apl_help/ch_020_020_330.htm APLX]
* [http://microapl.com/apl_help/ch_020_020_330.htm APLX]
* J [http://www.jsoftware.com/help/dictionary/d020.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/gt#dyadic NuVoc]
* J [http://www.jsoftware.com/help/dictionary/d020.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/gt#dyadic NuVoc]
* [https://mlochbaum.github.io/BQN/doc/arithmetic.html#comparisons BQN]


{{APL built-ins}}
{{APL built-ins}}[[Category:Primitive functions]][[Category:Comparison functions]]

Latest revision as of 22:07, 10 September 2022

Main article: Comparison function
>

Greater than (>) is a comparison function which tests whether the left argument is tolerantly greater than and not equal to the right argument, returning 1 if this is the case and 0 otherwise. It is the negation of Less than or Equal to ().

Boolean function

When the arguments to Greater than are Boolean, it is the material nonimplication Boolean function, also known as the NIMPLY gate:

> 0 1
0 0 0
1 1 0

In the context of logic, it can be read as but not.

External links

Documentation


APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare RootRound
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentityStopSelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndexCartesian ProductSort
Selector Index generatorGradeIndex OfInterval IndexIndicesDealPrefix and suffix vectors
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axisIdentity (Null, Ident)
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductDeterminantPowerAtUnderRankDepthVariantStencilCutDirect definition (operator)Identity (Lev, Dex)
Quad names Index originComparison toleranceMigration levelAtomic vector