: Axiom 4: If a property A is positive, then it is so in every possible world.

In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T < sub > 4 </ sub >: every two disjoint closed sets of X have disjoint open neighborhoods.

Axiom 4.

: Axiom 4.

* Volume 4: Axiom Developers Guide -- Short essays on developer-specific topics ( incomplete )

** Volume 10. 4: Axiom Algebra Packages -- Source code for Axiom packages

< ol >< li value =" 4 "> Pasch's Axiom: Let A, B, C be three points not lying in the same straight line and let a be a straight line lying in the plane ABC and not passing through any of the points A, B, C. Then, if the straight line a passes through a point of the segment AB, it will also pass through either a point of the segment BC or a point of the segment AC .</ li ></ ol >

* Old axiom II. 5 ( Pasch's Axiom ) is renumbered as II. 4.

** Axiom 4: High levels of uncertainty in a relationship cause decreases in the intimacy level of communication content.

Axiom 1: If a property is positive, then its negation is not positive.

Referring to the enemy's power supplies he wrote ( as Axiom 3 ): " If their destruction or paralysis can be accomplished they offer a means of rendering the enemy utterly incapable of continuing to prosecute the war ".

* Subset Property ( Axiom of Reflexivity ): If Y is a subset of X, then X → Y

* Augmentation ( Axiom of Augmentation ): If X → Y, then XZ → YZ

* Transitivity ( Axiom of Transitivity ): If X → Y and Y → Z, then X → Z

: AXIOM I. Axiom of extensionality ( Axiom der Bestimmtheit ) " If every element of a set M is also an element of N and vice versa ... then M N. Briefly, every set is determined by its elements ".

* Axiom of induction: If φ ( a ) is a formula, and if for all sets x it follows from the fact that φ ( y ) is true for all elements y of x that φ ( x ) holds, then φ ( x ) holds for all sets x.

# " If 6 Was 9 " ( Jimi Hendrix ) by Axiom Funk

Rather, we may form the set of all objects that have a given property and lie in some given set ( Zermelo's Axiom of Separation ).

Axiom 2: Any property entailed by — i. e., strictly implied by — a positive property is positive

Axiom 3: The property of being God-like is positive

Axiom 6: For any property P, if P is positive, then being necessarily P is positive.

: Axiom 3: The property of " being God-like ", G is a positive property.

: Axiom 5: Necessary existence is a positive property ( Pos ( NE )).

Assuming the Axiom of choice, is regular for each α.

Axiom 5: Necessary existence is positive

: Axiom 1: It is possible to single out positive properties from among all properties.

: Axiom 2: For all properties A, either A is positive or " not A " is positive.

Here is a quotation from a paper by Jan Łukasiewicz, Remarks on Nicod's Axiom and on " Generalizing Deduction ", page 180.

then, seen as a statement about cardinal numbers, it is equivalent to the Axiom of choice.

This is also known as Zermelo's theorem and is equivalent to the Axiom of Choice.

This condition is known as Axiom T < sub > 3 </ sub >.

The Axiom Ensemble is a student directed and managed group dedicated to well-known 20th century works.

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

However this particular method, involving differentiation of special functions with respect to its parameters, variable transformation, pattern matching and other manipulations, was pioneered by developers of the Maple system then later emulated by Mathematica, Axiom, MuPAD and other systems.

Axiom was ( at that moment ) shuttered as well, with most of the catalog falling out of print since then.

If the barn-burner's family produces a Flem Snopes, who personifies commercialism and materialism in hyperbolic crassness, the Compson family produces a Jason Compson 4.

If the universe is flat, there must be an additional component making up 73 % ( in addition to the 23 % dark matter and 4 % baryons ) of the energy density of the universe.

If the substituents are numbered from 1 ( highest priority ) to 4 ( lowest priority ), then the sense of rotation of a curve passing through 1, 2 and 3 distinguishes the stereoisomers.

If a 4, 5, 6, 8, 9, or 10 is thrown on the come-out roll ( i. e., if a point is set ), most casinos allow pass line bettors to take odds by placing from one to five times ( and at some casinos, up to 100 times ) the pass line bet behind the pass line.

If a 7 comes instead of the point coming, the odds pay at true odds of 1-to-2 if 4 or 10 is the point, 2-to-3 if 5 or 9 is the point, 5-to-6 if 6 or 8 is the point.

If instead the roll is 4, 5, 6, 8, 9, 10 then the come bet will be moved by the base dealer onto a box representing the number the shooter threw.

If instead the roll is 4, 5, 6, 8, 9, 10 then the don't come bet will be moved by the base dealer onto a box representing the number the shooter threw.

If the electrode has a positive potential with respect to the SHE, then that means it is a strongly reducing electrode which forces the SHE to be the anode ( an example is Cu in aqueous CuSO < sub > 4 </ sub > with a standard electrode potential of 0. 337 V ).

: Problem in words: If you double my son's age and add 4, the resulting answer is 12.

# If the remainder is 3, move 2 to the end of even list and 1, 3 to the end of odd list ( i. e. 4, 6, 8, 2-5, 7, 9, 1, 3 )

If the currently accepted figure of 11. 4 ly ( see 61 Cygni and discussion page ) is correct, Bessel's figure had an error of 8. 8 %.

If at least 50 cars had been built, sportscars like the GT40 and the Lola T70 were allowed, with a maximum of 5. 0 L. John Wyer's revised 4. 7 litre ( Bored to 4. 9 litres, and o-rings cut and installed between the deck and head to prevent head gasket failure, a common problem found with the 4. 7 engine.

If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional ( grassman -) Jordan algebra, which has the symmetry group of one of the exceptional Lie groups ( F < sub > 4 </ sub >, E < sub > 6 </ sub >, E < sub > 7 </ sub > or E < sub > 8 </ sub >) depending on the details.

If a gas powered pump can drain a pool in 4 hours and a battery powered pump can drain the same pool in 6 hours, then it will take both pumps

If a party represents more than 4 states then such parties are considered as national parties.

If all contracts awarded reach their stated target plateau production then this will increase Iraqi production from today's 2. 5 mb / d by 9. 4 mb / d to a total of 11. 9 mb / d, comparable to current Saudi declared capacity of 12. 5 mb / d.

If 4 workers each take six months off to re-train before they start a new job, the aggregate unemployment statistics will record this as two unemployed workers.

# Did the government agents obtain testimonial evidence as a result of the interrogation? If “ Yes ” go to 4 ; If “ No ”, Miranda does not apply.

If the project is completed, " more than 4, 000 km of waterways upstream from the dams in Brazil, Bolivia, and Peru would become navigable.

If there was life on Mars, after Mariner 4 most concluded it would probably be smaller, simpler forms.