* Axioms are propositions, the task of which is to make precise the notion of identity of two objects pre-existing in our mind.

Axioms are not taken as self-evident truths.

* ( 4 ) Axioms are neither experimental nor arbitrary, they force themselves on us since without them experience is not possible.

Axioms are usually regarded as starting points for applying rules of inference and generating a set of conclusions.

* Axioms are statements about these primitives, for example that any two points are together incident with just one line ( i. e. that for any two points, there is just one line which passes through both of them ).

By induction, Axioms ( 3 ) and ( 4 ) are equivalent to the single statement

Axioms or postulates are basic assertions assumed to be true.

Axioms are laid down in such a way that every first place member of d is a member of and every second place member is a finite subset of.

Axioms are propositions accepted as having no justification possible within the system.

There are two aphorisms that permit observers to calculate Variety ; four Principles of Organization ; the Recursive System Theorem ; three Axioms of Management and a Law of Cohesion.

( Axioms are statements ' worthy of belief ')

Axioms 1, 6, 7 and 8 imply that the set of natural numbers contains the distinct elements 0, S ( 0 ), S ( S ( 0 )), and so on ; i. e., it is informally known that

Category: Axioms of set theory

Category: Axioms of set theory

In modern set theory, we usually use the Von Neumann cardinal assignment which uses the theory of ordinal numbers and the full power of the Axioms of choice and replacement.

Category: Axioms of set theory

An extension of a set of points on a line with its order and congruence relations that would preserve the relations existing among the original elements as well as the fundamental properties of line order and congruence that follows from Axioms I-III, and from V. 1 is impossible.

Category: Axioms of set theory

Category: Axioms of set theory

" In Aphorism 21 of Book II, Bacon lays out the subsequent series of steps in proper induction: including Supports to Induction, Rectification of Induction, Varying the Inquiry according to the Nature of the Subject, Natures with Special Powers, Ends of Inquiry, Bringing Things down to Practice, Preparatives to Inquiry, and Ascending and Descending Scale of Axioms.

Note that the principle of sufficient reason can't be applied to Axioms within a logic construction like a mathematical or a physical theory.

The Peano Axioms ( described below ) thus only partially axiomatize this theory.

Possibility theory is computationally more convenient because Axioms 1-3 imply that:

These Dianetic " axioms " can be found in Hubbard books such as Scientology 0-8: The Book of Basics and Advanced Procedures and Axioms.

Axioms 1 and 6 define a unary representation of the natural numbers: the number 1 can be defined as S ( 0 ), 2 as S ( S ( 0 )) ( which is also S ( 1 )), and, in general, any natural number n as S < sup > n </ sup >( 0 ).

It might not be immediately clear whether another proof can be found that derives itself solely from the Peano Axioms.

For example, a number-theoretic statement might be expressible in the language of arithmetic ( i. e. the language of the Peano Axioms ) and a proof might be given that appeals to topology or complex analysis.

Absolute geometry assumes the first four of Euclid's Axioms ( or their equivalents ), to be contrasted with affine geometry, which does not assume Euclid's third and fourth axioms.

Moreover the consequences of large cardinal axioms seem to fall into natural patterns ( see Maddy, " Believing the Axioms, II ").

* Raymond Wilder ( 1965 ) Introduction to the Foundations of Mathematics 2nd edition, Chapter 2-8: Axioms defining equivalence, pp 48 – 50, John Wiley & Sons.

In the Axioms Scholium of his Principia Newton said its axiomatic three laws of motion were already accepted by mathematicians such as Huygens ( 1629 – 1695 ), Wallace, Wren and others, and also in memos in his draft preparations of the second edition of the Principia he attributed its first law of motion and its law of gravity to a range of historical figures.

There is the same degree of licentiousness and error in forming Axioms, as in abstracting Notions: and that in the first principles, which depend in common induction.

Still more is this the case in Axioms and inferior propositions derived from Syllogisms.

Vico ’ s Axioms: The Geometry of the Human World .. New Haven: Yale UP, 1995.

as at Propositional calculus # Axioms.

Axioms 1 through 6 were rediscovered by Italian-Japanese mathematician Humiaki Huzita and reported at the First International Conference on Origami in Education and Therapy in 1991.

Axioms 1 though 5 were rediscovered by Auckly and Cleveland in 1995.

Axioms specify the characteristics of classes and properties.

:::::: a. Axioms of Intuition

To you, for instance, the word innocence, in this connotation, probably retained its Biblical, or should I say technical sense, and therefore I suppose I must make myself quite clear by saying that I lost -- or rather handed over -- what you would have considered to be my innocence two weeks before I was legally entitled, and in fact by oath required, to hand it over along with what other goods and bads I had.

After complimenting Morgan and the riflemen and saying he was praising them to Congress, too, the ardent Frenchman added he felt that Congress should make some financial restitution to the widow and family of Morris, but that he knew Morgan realized how long such action usually required, if it was done at all.

The Secretary of the Treasury, upon the concurrence of the Secretary of State, is authorized and directed, out of the sum covered into the Yugoslav Claims Fund pursuant to subsection ( B ) of this section, after completing the payments of such funds pursuant to subsection ( C ) of this Section, to make payment of the balance of any sum remaining in such fund to the Government of the Federal People's Republic of Yugoslavia to the extent required under Article 1 ( C ) of the Yugoslav Claims Agreement of 1948.

If it is decided to make a small shift which may be required from military aid or special assistance funds, in order to carry out the purposes of the Mutual Security Act through this new peaceful program, this will be a hopeful sign to the world.

Place mold or paper pattern on rolled clay and cut clay by holding knife in vertical position ( cut more pieces than required for project to make allowance for defects ; ;

The temperature was maintained to within about Af for the period of time required to make the measurement ( usually about one hour ).

Most countries in this second category share the difficulty of having many of the structures of a modern political and social system without the modern standards of performance required to make them effective.

One day last week, Nixon faced a painful constitutional chore that required him to officiate at a joint session of Congress to hear the official tally of the Electoral College vote, and then to make `` sufficient declaration '' of the election of the man who defeated him in the tight 1960 presidential election.

The amounts required also depend on the age and health of the individual, so it is hard to make general statements about the dietary requirement for some amino acids.

ACSI opposed the Act primarily because the ADA labeled religious institutions " public accommodations ", and thus would have required churches to make costly structural changes to ensure access for all.

Moreover, those failing to do their duty are expected to make up planting requirements, provide funds equivalent to the value of labor required or pay heavy fines.

The proapoptotic homodimers are required to make the mitochondrial membrane permeable for the release of caspase activators such as cytochrome c and SMAC.

Anabaptists required that baptismal candidates be able to make their own confessions of faith and so rejected baptism of infants.

The Council recognized expert help was required to help shape what the town centre should look like over the next 10 – 15 years and how to make this happen.

If the assets used are not identical ( so a price divergence makes the trade temporarily lose money ), or the margin treatment is not identical, and the trader is accordingly required to post margin ( faces a margin call ), the trader may run out of capital ( if they run out of cash and cannot borrow more ) and go bankrupt even though the trades may be expected to ultimately make money.

However the dismasted Tonnant, Commodore Du Petit Thouars now dead from his wounds and thrown overboard at his own request, was unable to make the required speed and was driven ashore by its crew, while Timoléon was too far south to escape with Villeneuve and in attempting to join the survivors had also grounded on the shoal.

Every decision made by German or opposing forces required time to gather information, make a decision, disseminate orders to subordinates, and then implement this decision through action.

Bairoch points out that, due to sparse population densities that would have persisted in pre-Neolithic, hunter-gatherer societies, the amount of land that would be required to produce enough food for subsistence and trade for a large population would make it impossible to control the flow of trade.

Chemical accuracy is the accuracy required to make realistic chemical predictions and is generally considered to be 1 kcal / mol or 4 kJ / mol.

The shooter is required to make either a Pass Line bet or a Don't Pass bet if he wants to shoot.

* Activation energy, which is defined as the amount of energy required to make the reaction start and carry on spontaneously.

While Eddy's Manual established limited executive functions under the rule of law in place of a traditional hierarchy, the controversial 1991 publication of a book by Bliss Knapp led the then Board of Directors to make the unusual affidavit during a suit over Knapp's estate that neither acts by it violating the Manual, nor acts refraining from required action, constituted violations of the Manual.

For larger-scale enterprises, a complete and detailed plan is required to obtain the funding, resources, and company-wide support that can make the initiative of choosing and implementing a system successful.

The number of theoretical stages required to make a given separation is calculated using a specific vapor to liquid ratio.