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{{Built-in|Not Equal to|<nowiki>≠</nowiki>}} is a [[comparison function]] which tests whether argument elements are [[Tolerant comparison|tolerantly]] unequal. It is the [[Not|negation]] of [[Equal to]] (<syntaxhighlight lang=apl inline>=</ | {{Built-in|Not Equal to|<nowiki>≠</nowiki>}} is a [[comparison function]] which tests whether argument elements are [[Tolerant comparison|tolerantly]] unequal. It is the [[Not|negation]] of [[Equal to]] (<syntaxhighlight lang=apl inline>=</syntaxhighlight>). Thus it returns 0 if the [[element]]s being compared [[match]] and 1 if they do not. | ||
== Examples == | == Examples == | ||
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2 2.5 3 3.5 ≠ 2.5 | 2 2.5 3 3.5 ≠ 2.5 | ||
1 0 1 1 | 1 0 1 1 | ||
</ | </syntaxhighlight> | ||
== Boolean function == | == Boolean function == | ||
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When the arguments to Not Equal to are [[Boolean]], it is the [[wikipedia:exclusive or|exclusive or]] or xor function: | When the arguments to Not Equal to are [[Boolean]], it is the [[wikipedia:exclusive or|exclusive or]] or xor function: | ||
{|class=wikitable | {|class=wikitable | ||
!<syntaxhighlight lang=apl inline>≠</ | !<syntaxhighlight lang=apl inline>≠</syntaxhighlight>!!<syntaxhighlight lang=apl inline>0</syntaxhighlight>!!<syntaxhighlight lang=apl inline>1</syntaxhighlight> | ||
|- | |- | ||
!<syntaxhighlight lang=apl inline>0</ | !<syntaxhighlight lang=apl inline>0</syntaxhighlight> | ||
|<syntaxhighlight lang=apl inline>0</ | |<syntaxhighlight lang=apl inline>0</syntaxhighlight>||<syntaxhighlight lang=apl inline>1</syntaxhighlight> | ||
|- | |- | ||
!<syntaxhighlight lang=apl inline>1</ | !<syntaxhighlight lang=apl inline>1</syntaxhighlight> | ||
|<syntaxhighlight lang=apl inline>1</ | |<syntaxhighlight lang=apl inline>1</syntaxhighlight>||<syntaxhighlight lang=apl inline>0</syntaxhighlight> | ||
|} | |} | ||
Xor is one of the most important [[Boolean function]]s because it is equivalent to [[addition]] of the arguments with [[modulus]] 2. Like addition, it is [[wikipedia:Commutative property|commutative]] and [[wikipedia:Associative property|associative]]. It is also equivalent to [[subtraction]] with modulus 2 because the [[Minus|negative]] of a number is the same as the original number (mod 2): the negative of an odd number is still odd, and the negative of an even number is still even. | Xor is one of the most important [[Boolean function]]s because it is equivalent to [[addition]] of the arguments with [[modulus]] 2. Like addition, it is [[wikipedia:Commutative property|commutative]] and [[wikipedia:Associative property|associative]]. It is also equivalent to [[subtraction]] with modulus 2 because the [[Minus|negative]] of a number is the same as the original number (mod 2): the negative of an odd number is still odd, and the negative of an even number is still even. | ||
[[Reduction]] of a Boolean [[vector]] using Not Equal to yields 1 if there were an odd number of 1s in the argument and 0 otherwise. In APL, if <syntaxhighlight lang=apl inline>v</ | [[Reduction]] of a Boolean [[vector]] using Not Equal to yields 1 if there were an odd number of 1s in the argument and 0 otherwise. In APL, if <syntaxhighlight lang=apl inline>v</syntaxhighlight> is a Boolean vector then <syntaxhighlight lang=apl inline>≠/v</syntaxhighlight> {{←→}} <syntaxhighlight lang=apl inline>2|+/v</syntaxhighlight>. | ||
== External links == | == External links == | ||