A fourth level dyadic mathematic
operation involving exponentiation
There are two types; hyper4
is symbolized by either a^^b or a(4)
b, and is defined as a(4)
b = a^(a^(...^a)).
is symbolized by a(4)
and is defined as a(4)
b = ((a^a)^...)^a.
The former, hyper4
, definition is used more often as an independent operator
because the other, hyper4 operator
can be reduced
to double exponentiation
in the form: a(4)
b = a^(a^(b-1)), and thus is not really any different from exponentiation
. The hyper4 has not been extended to real numbers as addition
(1st level dyadic operation), multiplication
(2nd level) and exponentiation
(3rd level) have.
Alternate names for hyper4 can include: tetration
, and powerlog
This concept can be extended to the fifth degree and beyond as well, however each definition becomes recursive upon the last one...
I.e. hyper5 = a^^^b = a(5)
b = a(4)
or hyper6 = a^^^^b = a(6)
b = a(5)
For more information
on higher dyadic
P.S. If someone more knowledgeable wishes to rewrite this, feel free to do so.
This writeup is under the GNU Free Documentation License