Editing Nimber (section)

== Addition and multiplication tables ==
The following tables exhibit addition and multiplication among the first 16 nimbers.

This subset is closed under both operations, since 16 is of the form&nbsp;{{math|2<sup>2<sup>''n''</sup></sup>}}.
<small>(If you prefer simple text tables, they are {{Oldid|page=Nimber|oldid=383699838|label=here}}.)</small>

[[File:Z2^4; Cayley table; binary.svg|thumb|center|500px|Nimber addition {{OEIS|A003987}}<br>This is also the [[Cayley table]] of [[List of small groups#List of small abelian groups|Z<sub>2</sub><sup>4</sup>]] – or the table of [[Bitwise operation|bitwise]] [[w:Exclusive or|XOR]] operations.<br>The small matrices show the single digits of the binary numbers.]]

[[File:Nimbers 0...15 multiplication.svg|thumb|center|500px|Nimber multiplication {{OEIS|A051775}}<br>The nonzero elements form the [[w:Cayley table|Cayley table]] of [[w:List of small groups#List of small abelian groups|Z<sub>15</sub>]].<br>The small matrices are permuted binary [[Walsh matrix|Walsh matrices]].]]

[[File:Nimber products of powers of two.svg|thumb|center|900px|Nimber multiplication of [[Power of two|powers of two]] {{OEIS|A223541}}<br>Calculating the nim-products of powers of two is a decisive point in the recursive algorithm of nimber-multiplication.]]