: Precise instructions ( in language understood by " the computer ") for a fast, efficient, " good " process that specifies the " moves " of " the computer " ( machine or human, equipped with the necessary internally contained information and capabilities ) to find, decode, and then process arbitrary input integers / symbols m and n, symbols + and =

The best current ( 2009 ) estimate of the International Astronomical Union ( IAU ) for the value of the astronomical unit in meters is A = m, based on a comparison of JPL and IAA – RAS ephemerides.

The U. S. survey acre is about 4, 046. 872 609 874 252 square metres ; its exact value ( m < sup > 2 </ sup >) is based on an inch defined by 1 metre = 39. 37 inches exactly, as established by the Mendenhall Order.

: The part of the definition A ( m, 0 ) =

:: A ( m, n ) = hyper ( 2, m, n + 3 ) − 3.

:: 2 → n → m =

:( n = 1 and n = 2 would correspond with A ( m ,− 2 ) = − 1 and A ( m ,− 1 ) = 1, which could logically be added.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

An example is ƒ ( x ) = x − 1 / x, which has the oblique asymptote y = x ( m = 1, n = 0 ) as seen in the limits

* completely additive if a ( mn ) = a ( m ) + a ( n ) for all natural numbers m and n ;

* completely multiplicative if a ( mn ) = a ( m ) a ( n ) for all natural numbers m and n ;

* additive if a ( mn ) = a ( m ) + a ( n ) for all coprime natural numbers m and n ;