: 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 =

: For an example of the simple algorithm " Add m + n " described in all three levels see Algorithm examples.

Atomic orbitals are typically categorized by n, l, and m quantum numbers, which correspond to the electron's energy, angular momentum, and an angular momentum vector component, respectively.

Each orbital is defined by a different set of quantum numbers ( n, l, and m ), and contains a maximum of two electrons each with their own spin quantum number.

A given ( hydrogen-like ) atomic orbital is identified by unique values of three quantum numbers: n, l, and m < sub > l </ sub >.

In Analytical Geometry a section of a line can be given by the formula where ( c, d )&( e, f ) are the endpoints of the line & m: n is the ratio of division

S ( a, b )=( nc + me / m + n, nd + mf / m + n )

where m and n are nonnegative integers with, is the azimuthal angle in radians, and is the normalized radial distance.

One common version, the two-argument Ackermann – Péter function, is defined as follows for nonnegative integers m and n:

Ackermann's original three-argument function is defined recursively as follows for nonnegative integers m, n, and p:

Of the various two-argument versions, the one developed by Péter and Robinson ( called " the " Ackermann function by some authors ) is defined for nonnegative integers m and n as follows:

However, the recursion is bounded because in each recursive application either m decreases, or m remains the same and n decreases.

Each time that n reaches zero, m decreases, so m eventually reaches zero as well.

( Expressed more technically, in each case the pair ( m, n ) decreases in the lexicographic order on pairs, which is a well-ordering, just like the ordering of single non-negative integers ; this means one cannot go down in the ordering infinitely many times in succession.

) However, when m decreases there is no upper bound on how much n can increase — and it will often increase greatly.

:: A ( m, n )

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

:: A ( m, n )

:: 2 → n → m =

In modern notation this says that given quantities p, q, r and s, then p: q :: r: s if for any positive integers m and n, np < mq, np = mq, np > mq according as nr < ms, nr = ms, nr > ms respectively.

:: w-šnt lmʼš ʼlm b-bty šnt km h kkb m ʼl.

:: Georges Shoal, in 56-foot ( 17 m ) deep water, 110 miles ( 180 km ) east of Cape Cod 41 ° 44 ′ N 67 ° 47 ′ W  /  41. 733 ° N 67. 783 ° W  / 41. 733 ;-67. 783 , linked to North Truro, MA.

:: Nantucket Shoals, in 80-foot ( 24 m ) water, 100 miles ( 160 km ) south-east of Rhode Island 40 ° 45 ′ N 69 ° 19 ′ W  /  40. 75 ° N 69. 317 ° W  / 40. 75 ;-69. 317 , linked to Montauk AFB, Long Island, NY.

:: Un-named Shoal ( Unofficially: Old Shaky ), in 185-foot ( 56 m ) water, 84 miles ( 135 km ) south-east of New York City 39 ° 48 ′ N 72 ° 40 ′ W ( Destroyed, with 28 killed, during a storm on 15 January 1961 ), linked to Highlands, NJ mainland station.

:: 0 → E < sub > 0 </ sub > → E < sub > 1 </ sub > → E < sub > 2 </ sub > → ... → E < sub > m </ sub > → 0

:: 1500 m flight visibility, Clear of cloud and with the surface in sight.

:: Male 2. 26 m ( 7 ' 5 ")

:: Female 2. 29 m ( 7 ' 6 ")

:: m < sub > ħ </ sub > ≈ 1. 1 ( Ω < sub > ħ </ sub >/ Ω < sub > DM </ sub >)< sup > ½ </ sup > TeV

:: All types of K1 Minimum length 3. 50 m minimum width 0. 60 m

:: All types of C1 Minimum length 3. 50 m minimum width 0. 65 m

:: All types of C2 Minimum length 4. 10 m minimum width 0. 75 m

:: τ < sub > N · m </ sub > is the torque in newton metres

:: m

real :: A ( m, n )!

:: n is an integer

define method factorial ( n :: < integer >)

:: ( C < sub > 6 </ sub > H < sub > 4 </ sub >)( CO < sub > 2 </ sub > CH < sub > 3 </ sub >)< sub > 2 </ sub > + 2 C < sub > 2 </ sub > H < sub > 4 </ sub >( OH )< sub > 2 </ sub > → 1 / n

:: to show / solve < tt > G </ tt >, show / solve < tt > G < sub > 1 </ sub ></ tt > and … and < tt > G < sub > n </ sub ></ tt >

:: Let n = 0

:: Example: See also Martin v. Wilks, 490 U. S. 755, 784 n. 21, 104 L. Ed.

:: n < sub > x </ sub >, n < sub > y </ sub >, n < sub > z </ sub > are positive integers.

:: is a residue modulo p < sup > n </ sup > if k ≥ n

:: is a nonresidue modulo p < sup > n </ sup > if k < n is odd

:: is a residue modulo p < sup > n </ sup > if k < n is even and A is a residue

:: is a nonresidue modulo p < sup > n </ sup > if k < n is even and A is a nonresidue.

:: 1 ) Leipzig: Breitkopf & Härtel, n. d., cat.