Add: Difference between revisions
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Miraheze>Adám Brudzewsky |
Miraheze>Adám Brudzewsky |
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Addition is [https://en.wikipedia.org/wiki/Commutative_property commutative] in almost all number systems. It is [https://en.wikipedia.org/wiki/Associative_property associative] when performed with no rounding, but is unlikely to be associative when rounded to an inexact precision (see [[#Floating point error|Floating point error]]). | Addition is [https://en.wikipedia.org/wiki/Commutative_property commutative] in almost all number systems. It is [https://en.wikipedia.org/wiki/Associative_property associative] when performed with no rounding, but is unlikely to be associative when rounded to an inexact precision (see [[#Floating point error|Floating point error]]). | ||
The [[identity element]] for Add is <source lang=apl inline>0</source>. The [[inverse]] of the function <source lang=apl inline>n∘+</source> or the equivalent function <source lang=apl inline>+∘n</source> is <source lang=apl inline>-∘n</source>. Using [[Commute]] (<source lang=apl inline>⍨</source>), we can write <source lang=apl inline>+⍣¯1 ←→ -⍨</source>. | The [[identity element]] for Add is <source lang=apl inline>0</source>. The [[inverse]] of the function <source lang=apl inline>n∘+</source> or the equivalent function <source lang=apl inline>+∘n</source> is <source lang=apl inline>-∘n</source>. Using [[Commute]] (<source lang=apl inline>⍨</source>), we can write <source lang=apl inline>+⍣¯1</source> {{←→}} <source lang=apl inline>-⍨</source>. | ||
== Scalar mapping == | == Scalar mapping == | ||