As the total number of incepting bachelors in 1629 was, according to Masson ( Life, 1:218 ) and n, two hundred fifty-nine, the twenty-four names listed in the ordo senioritatis for that year constitute slightly less than one tenth of the total number of bachelors who then incepted.

But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.

: 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 =

An important class of alcohols are the simple acyclic alcohols, the general formula for which is C < sub > n </ sub > H < sub > 2n + 1 </ sub > OH.

A formula for calculating the variance of an entire population of size n is:

A formula for calculating an unbiased estimate of the population variance from a finite sample of n observations is:

for i in range ( n ):

for i in range ( n ):

In the quantum picture of Heisenberg, Schrödinger and others, the Bohr atom number n for each orbital became known as an n-sphere in a three dimensional atom and was pictured as the mean energy of the probability cloud of the electron's wave packet which surrounded the atom.

In number theory, if P ( n ) is a property of positive integers, and if p ( N ) denotes the number of positive integers n less than N for which P ( n ) holds, and if

( see limit ), then we say that " P ( n ) holds for almost all positive integers n " ( formally, asymptotically almost surely ) and write

Clearly there is always at least one such string for any n, as otherwise all possible strings ( infinitely many ) could be generated by the ( finitely many ) programs with lower complexity, so GenerateComplexString must always return.

The hostility to Agnes, it must be admitted, may be exaggerated by the chronicler William of Tyre, whom she prevented from becoming Latin Patriarch of Jerusalem decades later, as well as from William's continuators like Ernoul, who hints at a slight on her moral character: " car telle n ' est que roine doie iestre di si haute cite comme de Jherusalem " (" there should not be such a queen for so holy a city as Jerusalem ").

Thus two indices are used for a two dimensional array, three for a three dimensional array, and n for an n dimensional array.

Two results which follow from the axiom are that " no set is an element of itself ," and that " there is no infinite sequence ( a < sub > n </ sub >) such that a < sub > i + 1 </ sub > is an element of a < sub > i </ sub > for all i. "

AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O ( log n ) time for the basic operations.

The number of neutrons, N, is known as the neutron number of the atom ; thus, A = Z + N. Since protons and neutrons have approximately the same mass ( and the mass of the electrons is negligible for many purposes ), and the mass defect is usually very small compared to the mass, the atomic mass of an atom is roughly equal to A.

This central charge would thus be approximately half the atomic weight ( though it was almost 25 % off the figure for the atomic number in gold ( Z = 79, A = 197 ), the single element from which Rutherford made his guess ).

The binding energy needed for a nucleon to escape the nucleus, for various isotopes | deadurl = no

Since p ( x ) is irreducible, this means that p ( x ) = k ( x − a ), for some k ∈ F

The advantage of spherical coordinates ( for atoms ) is that an orbital wave function is a product of three factors each dependent on a single coordinate: ψ ( r, θ, φ ) = R ( r ) Θ ( θ ) Φ ( φ ).

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 1976 definition of the astronomical unit was incomplete, in particular because it does not specify the frame of reference in which time is to be measured, but proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity was proposed, and " vigorous debate " ensued until in August 2012 the International Astronomical Union adopted the current definition of 1 astronomical unit = 149597870700 meters.

Anagrams are also often used in fiction for character aliases, such as Tom Marvolo Riddle = I am Lord Voldemort, Leonardo da vinci = O Draconian Devil, The Mona Lisa

Under Ambrose's major influence, emperors Gratian, Valentinian II and Theodosius I carried on a persecution of Paganism .< ref name = " MacMullen1984p100 "> MacMullen ( 1984 ) p. 100: ‘ The law of June 391, issued by Theodosius [...] was issued from Milan and represented the will of its bishop, Ambrose ; for Theodosius — recently excommunicated by Ambrose, penitent, and very much under his influence < sup > 43 </ sup > — was no natural zealot.

At temperatures near 0 K, nearly all molecular motion ceases and, when entropy = S, ΔS = 0 for any adiabatic process.

dQ = TdS = 0 holds for reversible processes only.

100 cc and P = 2. 50E6 pascals, so we can solve for temperature by simple algebra:

In the later play Frogs, Aristophanes softens his criticisms, but even so it may be only for the sake of punning on Agathon's name ( ἁγαθός = " good ") that he makes Dionysus call him a " good poet ".

Ayckbourn joined Wolfit on tour to the Edinburgh Festival Fringe as an acting assistant stage manager ( meaning a role that involved both acting and stage management ) for three weeks, with his first role on the professional stage being various parts in The Strong are Lonely by Fritz Hochwälder .< ref name = acting >

These points form a line, and y = x is said to be the equation for this line.

The equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = r < sup > 2 </ sup > is the equation for any circle with a radius of r.

In general, if y = f ( x ), then it can be transformed into y = af ( b ( x − k )) + h. In the new transformed function, a is the factor that vertically stretches the function if it is greater than 1 or vertically compresses the function if it is less than 1, and for negative a values, the function is reflected in the x-axis.

These aberrations are avoided if, according to Abbe, the sine condition, sin u ' 1 / sin u1 = sin u ' 2 / sin u2, holds for all rays reproducing the point O.

When Af for each i, we shall have Af, because the operator Af will then be 0 on the range of Af.

for, using the fact that N and N' commute Af and so when R is sufficiently large every term in this expression for Af will be 0.

However much football has been over-emphasized, the public likes to measure its collegiate favorites by the scoreboard, so, while Yale need never give its record a thought again since outscoring its opponents 694 to 0 in the season of 1888, Dartmouth had to wait until its championship team of 1925 for national recognition.

Cohen ( 1992 ) suggests effect sizes for various indexes, including ƒ ( where 0. 1 is a small effect, 0. 25 is a medium effect and 0. 4 is a large effect ).

He also offers a conversion table ( see Cohen, 1988, p. 283 ) for eta squared ( η < sup > 2 </ sup >) where 0. 0099 constitutes a small effect, 0. 0588 a medium effect and 0. 1379 a large effect.

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

West Indies defeated England twice in the mid-1960s and South Africa, in two series before they were banned for apartheid, completely outplayed Australia 3 – 1 and 4 – 0.

He made the first measurement of stellar parallax: 0. 3 arcsec for the binary star 61 Cygni.

Today, the catalogue most often used is USNO-B1. 0, an all-sky catalogue that tracks proper motions, positions, magnitudes and other characteristics for over one billion stellar objects.

The attributes run from-25 ( normal human level ), through-10 ( normal level for a denizen of the Courts of Chaos ) and 0 ( normal level for an inhabitant of Amber ), upwards without limit.

These states are labeled by a set of quantum numbers summarized in the term symbol and usually associated with particular electron configurations, i. e., by occupation schemes of atomic orbitals ( e. g., 1s < sup > 2 </ sup > 2s < sup > 2 </ sup > 2p < sup > 6 </ sup > for the ground state of neon -- term symbol: < sup > 1 </ sup > S < sub > 0 </ sub >).

The original Nernst heat theorem makes the weaker and less controversial claim that the entropy change for any isothermal process approaches zero as T → 0:

One century later, their use of the symbols which became 2, 7 and 9 was recorded, but Brahmi numerals lacked a symbol for 0.

** ( Actual approximately − 11. 0 ) The diffuse reflector formula does for smaller phases.

While over the far side of the Moon, the Command / Service Module's Service Propulsion System engine burned for six minutes and fifteen seconds, braking the spacecraft into an orbit around the Moon with a low point ( pericynthion ) of 58. 3 and a high point ( apocynthion ) of 170. 4 nautical miles ( 108. 0 and 315. 6 km, respectively ).

In a 2D image element, which stores a color for each pixel, additional data is stored in the alpha channel with a value between 0 and 1.