Not Equal to: Difference between revisions

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== Boolean function ==
== Boolean function ==


When the arguments to Not Equal to are [[Boolean]], it is the [[wikipedia:exclusive or|exclusive or]] or xor function. 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.
When the arguments to Not Equal to are [[Boolean]], it is the [[wikipedia:exclusive or|exclusive or]] or xor function:
{|class=wikitable
!<source lang=apl inline>≠</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source>
|-
!<source lang=apl inline>0</source>
|<source lang=apl inline>0</source>||<source lang=apl inline>1</source>
|-
!<source lang=apl inline>1</source>
|<source lang=apl inline>1</source>||<source lang=apl inline>0</source>
|}
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 <source lang=apl inline>v</source> is a Boolean vector then <source lang=apl inline>≠/v</source> {{←→}} <source lang=apl inline>2|+/v</source>.
[[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 <source lang=apl inline>v</source> is a Boolean vector then <source lang=apl inline>≠/v</source> {{←→}} <source lang=apl inline>2|+/v</source>.

Revision as of 08:47, 29 March 2020

≠

Not Equal to (≠) is a comparison function which tests whether argument elements are tolerantly unequal. It is the negation of Equal to (=). Thus it returns 0 if the elements being compared match and 1 if they do not.

Examples

See Equal to for a more detailed treatment of equality testing. 

      2 2.5 3 3.5 ≠ 2.5
1 0 1 1

Boolean function

When the arguments to Not Equal to are Boolean, it is the exclusive or or xor function:

≠ 0 1
0 0 1
1 1 0

Xor is one of the most important Boolean functions because it is equivalent to addition of the arguments with modulus 2. Like addition, it is commutative and associative. It is also equivalent to subtraction with modulus 2 because the 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 v is a Boolean vector then ≠/v 2|+/v.

External links

Documentation


APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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