Dismal arithmetic

Definition

Dismal arithmetic is a commutative algebra in which operations on single digits are defined by

$a\oplus b=\max\{a,b\},a\otimes b=\min\{a,b\}\,$

or equivalently

$a\oplus b=\lim _{k\to \infty }{\sqrt[{k}]{a^{k}+b^{k}}},a\otimes b=\lim _{k\to \infty }{\frac {1}{\sqrt[{k}]{{\tfrac {1}{a^{k}}}+{\tfrac {1}{b^{k}}}}}}\,$

See also

• Carryless arithmetic mod 10

References

• [ALS] David Applegate, Marc LeBrun, N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version, 2010.