It would challenge sharply not the cult of the motor car itself but some of its ancillary beliefs and practices -- for instance, the doctrine that the fulfillment of life consists in proceeding from hither to yon, not for any advantage to be gained by arrival but merely to avoid the cardinal sin of stasis, or, as it is generally termed, staying put.

I wrote a few years ago that one of the cardinal rules of writing is that the reader should be able to get some idea of what the story is about.

The only cardinal sin which may be committed in warming a wine is to force it by putting it next to the stove or in front of an open fire.

He has a pleasant sense of humor and is modest enough to admit mistakes and even `` a cardinal error ''.

It is also consistent with ZF + DC that every set of reals is Lebesgue measurable ; however, this consistency result, due to Robert M. Solovay, cannot be proved in ZFC itself, but requires a mild large cardinal assumption ( the existence of an inaccessible cardinal ).

ZF + DC + AD is consistent provided that a sufficiently strong large cardinal axiom is consistent ( the existence of infinitely many Woodin cardinals ).

One of the highlights of the facade is a tower topped with a cross of four arms oriented to the cardinal directions.

Related to the argument from morality is the argument from conscience, associated with eighteenth-century bishop Joseph Butler and nineteenth-century cardinal John Henry Newman.

This is a building with circular tower and doors facing the cardinal directions.

; Cardinal: In Roman Catholicism, a cardinal is a member of the clergy appointed by the pope to serve in the College of Cardinals, the body empowered to elect the pope ; however, on turning 80 a cardinal loses this right of election.

Under modern canon law, a man who is appointed a cardinal must accept ordination as a bishop, unless he already is one, or seek special permission from the pope to decline such ordination.

The Roman Breviary has undergone several revisions: The most remarkable of these is that by Francis Quignonez, cardinal of Santa Croce in Gerusalemme ( 1536 ), which, though not accepted by Rome ( it was approved by Clement VII and Paul III, and permitted as a substitute for the unrevised Breviary, until Pius V in 1568 excluded it as too short and too modern, and issued a reformed edition ( Breviarium Pianum, Pian Breviary ) of the old Breviary ), formed the model for the still more thorough reform made in 1549 by the Church of England, whose daily morning and evening services are but a condensation and simplification of the Breviary offices.

The walls defining the enclosures of Khmer temples are frequently lined by galleries, while passage through the walls is by way of gopuras located at the cardinal points.

" Venerable / Heroic in Virtue " When enough information has been gathered, the congregation will recommend to the pope that he make a proclamation of the Servant of God's heroic virtue ( that is, that the servant exhibited the theological virtues of faith, hope and charity, and the cardinal virtues of prudence, justice, fortitude and temperance, to a heroic degree ).

* The cardinal is also a fairy chess piece, also known as the archbishop

Two sets have the same cardinal number if and only if there is a bijection between them.

A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the set of real numbers and the set of natural numbers do not have the same cardinal number.

There is a transfinite sequence of cardinal numbers:

In set theory, an uncountable regular cardinal number is called weakly inaccessible if it is a weak limit cardinal, and strongly inaccessible, or just inaccessible, if it is a strong limit cardinal.

Until about 1950 it meant " weakly inaccessible cardinal ", but since then it usually means " strongly inaccessible cardinal ".

Every strongly inaccessible cardinal is also weakly inaccessible, as every strong limit cardinal is also a weak limit cardinal.

If the generalized continuum hypothesis holds, then a cardinal is strongly inaccessible if and only if it is weakly inaccessible.

However, only a rather large cardinal number can be both and thus weakly inaccessible.

An ordinal is a weakly inaccessible cardinal if and only if it is a regular ordinal and it is a limit of regular ordinals.

) A cardinal which is weakly inaccessible and also a strong limit cardinal is strongly inaccessible.

Thus ZF together with " there exists a weakly inaccessible cardinal " implies that ZFC is consistent.

A real valued measurable cardinal is weakly Mahlo.

In mathematics, a weakly compact cardinal is a certain kind of cardinal number introduced by ; weakly compact cardinals are large cardinals, meaning that their existence can not be proven from the standard axioms of set theory.

Formally, a cardinal κ is defined to be weakly compact if it is uncountable and for every function f: < sup > 2 </ sup > →

A Shelah cardinal has a normal ultrafilter containing the set of weakly hyper-Woodin cardinals below it.

A cardinal k is κ-strongly unfoldable, and κ-unfoldable, if and only if it is weakly compact.

This is not an axiom of infinity in the usual sense ; if Infinity does not hold, the closure of exists and has itself as its sole additional member ( it is certainly infinite ); the point of this axiom is that contains no additional elements at all, which boosts the theory from the strength of second order arithmetic to the strength of Morse – Kelley set theory with the proper class ordinal a weakly compact cardinal.

It in fact interprets a stronger theory ( Morse-Kelley set theory with the proper class ordinal a weakly compact cardinal ).

The following definition generalises the definitions of compact and Lindelöf: a topological space is-compact ( or-Lindelöf ), where is any cardinal, if every open cover has a subcover of cardinality strictly less than.

In mathematical set theory, a strongly compact cardinal is a certain kind of large cardinal number.

A cardinal κ is strongly compact if and only if every κ-complete filter can be extended to a κ complete ultrafilter.

The logic on a regular cardinal κ is defined by requiring the number of operands for each operator to be less than κ ; then κ is strongly compact if its logic satisfies an analog of the compactness property of finitary logic.

Given that the relevant cardinals exist, it is consistent with ZFC either that the first measurable cardinal is strongly compact, or that the first strongly compact cardinal is supercompact ; these cannot both be true, however.

Some set theorists conjecture that existence of a strongly compact cardinal is equiconsistent with that of a supercompact cardinal.

Confucianism holds that one should give up one's life, if necessary, either passively or actively, for the sake of upholding the cardinal moral values of ren and yi.

Two sets are said to have the same cardinality or cardinal number if there exists a bijection ( a one-to-one correspondence ) between them.

Confucianism holds that one should give up one's life, if necessary, either passively or actively, for the sake of upholding the cardinal moral values of ren and yi.

Barry Mitchell has shown ( in " The cohomological dimension of a directed set ") that if I has cardinality ( the dth infinite cardinal ), then R < sup > n </ sup > lim is zero for all n ≥ d + 2.

However, if an inaccessible cardinal κ is assumed, then the sets of smaller rank form a model of ZF ( a Grothendieck universe ), and its subsets can be thought of as " classes ".

More generally, if κ is any infinite cardinal, then a product of at most 2 < sup > κ </ sup > spaces with dense subsets of size at most κ has itself a dense subset of size at most κ ( Hewitt – Marczewski – Pondiczery theorem ).

The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural numbers.

He boasted that if elected pope he would buy each cardinal a villa to escape the summer heat.

A cardinal Grand Cross is said to cause a particular difficulty in accomplishing goals because the individual wants to accomplish everything at the same time: he / she usually ends up accomplishing very little ( if anything at all ).

of random variables is said to be exchangeable if for any finite cardinal number n and any two finite sequences i < sub > 1 </ sub >, ..., i < sub > n </ sub > and j < sub > 1 </ sub >, ..., j < sub > n </ sub > ( with each of the is distinct, and each of the js distinct ), the two sequences

In set theory, König's theorem ( named after the Hungarian mathematician Gyula Kőnig, who published under the name Julius König ) colloquially states that if the Axiom of Choice holds, I is a set, m < sub > i </ sub > and n < sub > i </ sub > are cardinal numbers for every i in I, and < math > m_i < n_i

This follows from Gödel's second incompleteness theorem, which shows that if ZFC + " there is an inaccessible cardinal " is consistent, then it cannot prove its own consistency.