But the real beginnings of this development in him go back to the opposing of grammar school, and probably if it had not been this occasion and these Latin lines it would have been some others, such as the first prolusion, that set off this streak in him of unbridled and scathing verbal attack on an enemy.

After the usual Honorable Sirs, it went on to say that there had been set off to the widow one full third part of the real estate of the deceased Salu Norberg, one lower room, on the Western side, privileges to the well and bake-oven and to one third of the cellar ( I can show you the cellar when we go up ), also one Cow Right, and lastly they set off to the widow her own land that she brought with her as dower, namely the Beech Pasture.

The tragic irony of the play is that the very belief in and concern with a devil who could be met in the woods and combatted with formulae set out in books was the very thing that prevented them from detecting the real devil when he came among them.

This did not set Gershwin back, as his real intent abroad was to complete a new work based on Paris and perhaps a second rhapsody for piano and orchestra.

For example, suppose that X is the set of all non-empty subsets of the real numbers.

For example, while the axiom of choice implies that there is a well-ordering of the real numbers, there are models of set theory with the axiom of choice in which no well-ordering of the reals is definable.

Similarly, although a subset of the real numbers that is not Lebesgue measurable can be proven to exist using the axiom of choice, it is consistent that no such set is definable.

For example, if we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬ AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets.

Basic theories, such as arithmetic, real analysis and complex analysis are often introduced non-axiomatically, but implicitly or explicitly there is generally an assumption that the axioms being used are the axioms of Zermelo – Fraenkel set theory with choice, abbreviated ZFC, or some very similar system of axiomatic set theory like Von Neumann – Bernays – Gödel set theory, a conservative extension of ZFC.

The real numbers are uniquely picked out ( up to isomorphism ) by the properties of a Dedekind complete ordered field, meaning that any nonempty set of real numbers with an upper bound has a least upper bound.

* The set of real algebraic numbers is linearly ordered, countable, densely ordered, and without first or last element, so is order-isomorphic to the set of rational numbers.

Area can be defined through the use of axioms, defining it as a function of a collection of certain plane figures to the set of real numbers.

Area can be defined as a function from a collection M of special kind of plane figures ( termed measurable sets ) to the set of real numbers which satisfies the following properties:

" Amazing Grace " set to " New Britain " was included in two hymnals distributed to soldiers and with death so real and imminent, religious services in the military became commonplace.

In number theory, an arithmetic, arithmetical, or number-theoretic function is a real or complex valued function ƒ ( n ) defined on the set of natural numbers ( i. e. positive integers ) that " expresses some arithmetical property of n ."

* Since Big Brother 2, the UK series always opens with a twist which have included the public being able to choose the final housemate out of three possibilities ( Big Brother 2 ), the public voting for a housemate to leave during the first week and then the housemates choosing between the two housemates with the least number of votes ( Big Brother 3 ), First Night Nominations ( Big Brother 4 ), Suitcase Nominations ( Big Brother 5 ), Unlucky Housemate 13 ( Big Brother 6 ), Big Brother Hood ( Big Brother 7 ), an all-female House and the first inclusion of twins as contestants ( Big Brother 8 ), the first couple to enter as housemates and set a secret task to hide their real relationship ( Big Brother 9 ), all " housemates " really being " non-housemates " who had to earn their housemate status ( Big Brother 10 ), a mole entering the House with an " Impossible Task " ( Big Brother 11 ), Jackie Stallone entering a house containing her son's ex-wife ( Celebrity Big Brother 3 ), the entrance of a non-celebrity in a celebrity edition ( Celebrity Big Brother 4 ) and Jade Goody's family announced to be visiting.

* The set of all real or complex n-by-n matrices becomes a unital Banach algebra if we equip it with a sub-multiplicative matrix norm.

: There is no set whose cardinality is strictly between that of the integers and that of the real numbers.

The President had set for himself the task, which he believed vital, of awakening the U. S. and its allies to the hard and complex effort necessary to shift that balance.

* Hence, the set of algebraic numbers has Lebesgue measure zero ( as a subset of the complex numbers ), i. e. " almost all " complex numbers are not algebraic.

The apical complex consists of a set of spirally arranged microtubules ( the conoid ), a secretory body ( the rhoptry ) and one or more polar rings.

A complex, aberrated wavefront profile may be curve-fitted with Zernike polynomials to yield a set of fitting coefficients that individually represent different types of aberrations.

The involvement of Athens in the Ionian Revolt arose from a complex set of circumstances, beginning with the establishment of the Athenian Democracy in the late 6th century BC.

Under this point of view, often attributed to James McClelland and David Rumelhart, the mind could be characterized as a set of complex associations, represented as a layered network.

is in C. In other words, every point on the line segment connecting x and y is in C. This implies that a convex set in a real or complex topological vector space is path-connected, thus connected.

Carnivory was a natural transition from insectivory for medium and large tetrapods, requiring minimal adaptation ( in contrast, a complex set of adaptations was necessary for feeding on highly fibrous plant materials ).

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.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

A complex instruction set computer ( CISC, ) is a computer where single instructions can execute several low-level operations ( such as a load from memory, an arithmetic operation, and a memory store ) and / or are capable of multi-step operations or addressing modes within single instructions.

The definable complex numbers also form a field if they form a set.

It is difficult to provide a single concise definition for dharma, as the word has a long and varied history and straddles a complex set of meanings and interpretations.

with C denoting the set of complex numbers.

form an orthogonal basis over the set of N-dimensional complex vectors:

The result is a more complex set of 3 equations.

Alpha, originally known as Alpha AXP, is a 64-bit reduced instruction set computer ( RISC ) instruction set architecture ( ISA ) developed by Digital Equipment Corporation ( DEC ), designed to replace the 32-bit VAX complex instruction set computer ( CISC ) ISA and its implementations.

** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).

The standard structure is where is the set of natural numbers, is the successor function and is naturally interpreted as the number 0.

* The set of algebraic numbers is countable ( enumerable ).

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.

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 >).

Because of the quantum mechanical nature of the electrons around a nucleus, atomic orbitals can be uniquely defined by a set of integers known as quantum numbers.

Some large telephone companies have toll-free numbers set up.

These numbers are set up by a company offering low charge calls in the UK, these numbers are meant to be used as a sort of operator that you go through in order to qualify for these cheap calls.