A mural artist is only limited by the fee and therefore the time spent on the painting ; dictating the level of detail ; a simple mural can be added to the smallest of walls.

For a simple example of the first kind, consider the proposition, ¬ p: " there is no smallest rational number greater than 0 ".

The smallest nonabelian simple group is the alternating group A < sub > 5 </ sub > of order 60, and every simple group of order 60 is isomorphic to A < sub > 5 </ sub >.

The second smallest nonabelian simple group is the projective special linear group PSL ( 2, 7 ) of order 168, and it is possible to prove that every simple group of order 168 is isomorphic to PSL ( 2, 7 ).

The smallest simple perfect squared square was discovered by A. J. W. Duijvestijn using a computer search.

The smallest simple squared square forms the logo of the Trinity Mathematical Society.

The space between sand particles is larger than the smallest suspended particles, so simple filtration is not enough.

The rank of any k-vector is defined to be the smallest number of simple elements of which it is a sum.

They are the smallest of the five exceptional simple Lie groups.

: is the simple group of order 168, the second smallest non-abelian simple group, and is not an alternating group ; see PSL ( 2, 7 ).

Using the same ideas used in minimum / maximum algorithms, we can construct a simple, but inefficient general algorithm for finding the kth smallest or kth largest item in a list, requiring O ( kn ) time, which is effective when k is small.

One is the very simple fact that the real difficulty of representative government is how to make it representative, even in the smallest of small nationalities, even in the nearest parish council.

The compact group E < sub > 8 </ sub > is unique among simple compact Lie groups in that its non-trivial representation of smallest dimension is the adjoint representation ( of dimension 248 ) acting on the Lie algebra E < sub > 8 </ sub > itself ; it is also the unique one which has the following four properties: trivial center, compact, simply connected, and simply laced ( all roots have the same length ).

Locke, in An Essay Concerning Human Understanding ( 1690 ), had reduced data to its smallest part: the simple idea derived from sense.

On the smallest boats, a sheet is often a simple rope, pulled by hand ; on larger boats, usually on the mainsheet, it is often a system using several blocks to provide mechanical advantage.

The Idrisiyah, the smallest of the three Sufi orders, has few ritual requirements beyond some simple prayers and hymns.

The smallest normal simple magic cube is order 3.

A simple, non-anthropologist's explanation is that the close family is the smallest and closest segment, and will generally stand with each other.

) The smallest group < sup > 2 </ sup > F < sub > 4 </ sub >( 2 ) of type < sup > 2 </ sup > F < sub > 4 </ sub > is not simple, but it has a simple subgroup of index 2, called the Tits group ( named after the mathematician Jacques Tits ).

The smallest group < sup > 2 </ sup > G < sub > 2 </ sub >( 3 ) of type < sup > 2 </ sup > G < sub > 2 </ sub > is not simple, but it has a simple normal subgroup of index 3, isomorphic to SL ( 2, 8 ).

The commutator subgroup is important because it is the smallest normal subgroup such that the quotient group of the original group by this subgroup is abelian.

The fact that all currently known ( 2009 ) matter particles fit nicely into three copies of the smallest group representations of SU ( 5 ) and immediately carry the correct observed charges, is one of the first and most important reasons why people believe that a Grand Unified Theory might actually be realized in nature.

The units of grammar formed a " hierarchy ", a scale from " largest " to " smallest " which he proposed as: " sentence ", " clause ", " group / phrase ", " word " and " morpheme ".

A consequence of the theorem is that the order of any element a of a finite group ( i. e. the smallest positive integer number k with a < sup > k </ sup > = e, where e is the identity element of the group ) divides the order of that group, since the order of a is equal to the order of the cyclic subgroup generated by a.

This does not hold in general: given a finite group G and a divisor d of | G |, there does not necessarily exist a subgroup of G with order d. The smallest example is the alternating group G = A < sub > 4 </ sub >, which has 12 elements but no subgroup of order 6.

The Klein four-group is the smallest non-cyclic group.

Although the smallest group in terms of numbers, members of the plantocracy had links to British commercial interests in London and often enjoyed close ties to the governor, who was appointed by the monarch.

Within the unit cell is the asymmetric unit, smallest unit the crystal can be divided into using the crystallographic symmetry operations of the space group.

Imin's companions, Tata and Enel, later awoke groups of nine and twelve pairs respectively, and Imin decided that since his group was now the smallest and each group that he and his companions discovered was larger than the last, he would now choose third rather than first in order to make up the numbers.

However, only a further two groups were discovered, leaving none for Imin ; his group of fourteen thus became by far the smallest of the three Elven clans.

The number of Istro-Romanian speakers is very loosely estimated to be less than 500, the " smallest ethnic group in Europe " and listed among languages that are " seriously endangered " in the UNESCO Red Book of Endangered Languages.

To form a group with presentation < S | R >, the idea is to take F < sub > S </ sub > quotient by the smallest normal subgroup such that each element of R gets identified with the identity.

More generally, if S is a subset of a group G, then < S >, the subgroup generated by S, is the smallest subgroup of G containing every element of S, meaning the intersection over all subgroups containing the elements of S ; equivalently, < S > is the subgroup of all elements of G that can be expressed as the finite product of elements in S and their inverses.

The radius is calculated from the mass by assuming spheres of density Af except for the smallest particles, which must have a higher mass density to remain in the solar system in the presence of solar-radiation pressure.

a program is ' elegant ,' by which I mean that it's the smallest possible program for producing the output that it does "

In approximately 450 BCE, Democritus coined the term átomos (), which means " uncuttable " or " the smallest indivisible particle of matter ".

For example, the smallest pair of amicable numbers is ( 220, 284 ); for the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284 ; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.

In data transmission systems a byte is defined as a contiguous sequence of binary bits in a serial data stream, such as in modem or satellite communications, which is the smallest meaningful unit of data.

The economy of Bhutan, one of the world's smallest and least developed, is based on agriculture and forestry, which provide the main livelihood for more than 60 % of the population.

Urban Müller created brainfuck in 1993 with the intention of designing a language which could be implemented with the smallest possible compiler, inspired by the 1024-byte compiler for the FALSE programming language.

In this case, is the smallest σ-algebra that contains the open intervals of R. While there are many Borel measures μ, the choice of Borel measure which assigns for every interval is sometimes called " the " Borel measure on R. In practice, even " the " Borel measure is not the most useful measure defined on the σ-algebra of Borel sets ; indeed, the Lebesgue measure is an extension of " the " Borel measure which possesses the crucial property that it is a complete measure ( unlike the Borel measure ).

* The smallest general-purpose computers were the B700 " microprocessors " which were used both as stand-alone systems and as special-purpose data-communications or disk-subsystem controllers.

The smallest monosaccharides, for which n

The elementary reaction is the smallest division into which a chemical reaction can be decomposed to, it has no intermediate products.

This also makes fire the element with the smallest number of sides, and Plato regarded it as appropriate for the heat of fire, which he felt is sharp and stabbing, ( like one of the points of a tetrahedra ).

The cofinality of an ordinal α is the smallest ordinal δ which is the order type of a cofinal subset of α.

instrument which multiplied the fighting value of even the smallest forces, allowing them to outflank and avoid, to surprise and overpower, to retreat and escape according to the requirements of the moment.

* He believed the smallest piece of matter was an indestructible and indivisible particle which he called the " atom ".

The set of constructible numbers can be completely characterized in the language of field theory: the constructible numbers form the quadratic closure of the rational numbers: the smallest field extension of which is closed under square root and complex conjugation.

In 1910, Carmichael found the first and smallest such number, 561, which explains the name " Carmichael number ".

If S is an arbitrary set, then the set S < sup > N </ sup > of all sequences in S becomes a complete metric space if we define the distance between the sequences ( x < sub > n </ sub >) and ( y < sub > n </ sub >) to be, where N is the smallest index for which x < sub > N </ sub > is distinct from y < sub > N </ sub >, or 0 if there is no such index.

The units had a robust motherboard in a spacious case, reminiscent of the BBC Micro, and so were more tolerant of home-modification than some of their contemporaries, which often had their components crammed into the smallest possible space.

Despite this, a museum exhibit opened in his honor, in which its owner claims it to be the country's smallest Presidential Library.

" Thus, any activity of production ( which distributism holds to be the most important part of any economy ) ought to be performed by the smallest possible unit.

The lone exception to this pattern has been the very smallest category of bookseller, shops with between one and four employees, which appear to have withstood the trend.

Buckminsterfullerene is the smallest fullerene molecule containing pentagonal and hexagonal rings in which no two pentagons share an edge ( which can be destabilizing, as in pentalene ).