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Page "Dianetics" ¶ 16
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Some Related Sentences

These and axioms
These are equivalent in the sense that, in the presence of other basic axioms of set theory, they imply the axiom of choice and are implied by it.
These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.
These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of consistency and completeness of number theory.
These conditions are examples of separation axioms.
These assumptions are the elementary theorems of the particular theory, and can be thought of as the axioms of that field.
These axioms are still in common use to this day.
These conditions are examples of separation axioms and their further strengthenings define completely normal Hausdorff spaces, or T < sub > 5 </ sub > spaces, and perfectly normal Hausdorff spaces, or T < sub > 6 </ sub > spaces.
These are sometimes called Tychonoff separation axioms, after Andrey Tychonoff.
These conditions are examples of separation axioms.
These operations then satisfy all of the axioms for meets, joins, and complements in a Boolean algebra.
These do not provide a resolution to Hilbert's second question, however, because someone who doubts the consistency of Peano arithmetic is unlikely to accept the axioms of set theory ( which is much stronger ) to prove its consistency.
These three axioms are another way of saying that the binary operation is bilinear.
These types are specified by insisting on some further axioms, such as commutativity or associativity of the multiplication operation, which are not required in the broad definition of an algebra.
These basic beliefs cannot, by definition, be proven ( in the logical sense ) within the worldview precisely because they are axioms, and are typically argued from rather than argued for.
These are not a minimal set of axioms but rather the complete set of possible single folds.
These axioms provide semantics by allowing systems to infer additional information based on the data explicitly provided.
These two properties are called Weyl's axioms.
These are essentially the strongest known large cardinal axioms not known to be inconsistent in ZFC ; the axiom for Reinhardt cardinals is stronger, but is not consistent with the axiom of choice.
These conditions are separation axioms that are somewhat stronger than the more familiar Hausdorff axiom T < sub > 2 </ sub >.
These axioms are sound for standard second-order semantics.
These symbols act on certain rules of formation and are developed by inference from a set of axioms.
These expressions are called axioms, in the case of those previously supposed to be true, or theorems, in the case of those derived.
These axioms have been relatively useful for mathematical treatments of Schwarz-type QFTs, although it isn't clear that they capture the whole structure of Witten-type QFTs.
These axioms differ basically in whether or not they study a TQFT defined on a single fixed n-dimensional Riemannian / Lorentzian spacetime M or a TQFT defined on all n-dimensional spacetimes at once.

These and can
These seem about the only two ways in which the `` unhappy incident '' can now be closed.
These engines can be removed from a boat with relative ease, wherein lies their greatest advantage.
These can also move a short distance but at right angles to the tappets.
These are beginnings, but correctly learned they prepare for satisfying and exciting stunts that can be performed by a strong, flexible body ( we are not talking of eccentric extremes ).
These frequencies are amplified and detected by the FM receiver after each burst of transmitted energy and, after the `` pill '' has been calibrated, precise internal pressure indications can be obtained.
These factors can make the difference between waste and efficiency in any benefit program.
These experiments can be considered exploratory only.
These societies can expect to face difficult times.
These records, when systematically maintained, provide much information about the children, which the teacher can use in guidance, instruction, grouping, and reporting to parents.
These can be referred to as operational intelligence and environmental intelligence.
These theoretical relationships are more clearly illustrated in Fig. 7 and their sum can be seen to correlate in form with practical measurements made with the Hesiometer as illustrated in the first portion of Fig. 5 for the cutting mechanism.
These dynamic relationships, between what can be observed on the ground, as opposed to what can be observed by compiling many local observations remain fundamental in any kind of anthropology, whether cultural, biological, linguistic or archaeological.
These are not used in amoeboid movement, but are stiff skeletons on which organelles are supported or can move on.
These can range from simple spelling changes and word forms to switching the entire writing system itself, as when Turkey switched from the Arabic alphabet to a Turkish alphabet of Latin origin.
These finishes protect the adobe wall from water damage, but need to be reapplied periodically, or the walls can be finished with other nontraditional plasters providing longer protection.
These deficits can vary depending on which cerebellar structures have been damaged, and whether the lesion is bilateral or unilateral.
These include all quadratic surds, all rational numbers, and all numbers that can be formed from these using the basic arithmetic operations and the extraction of square roots.
These frequencies can be used to study geological phenomena such as earthquakes.
These are naturally in a ground state but can be excited
These constructions can convey shape, size, motion, location, movement, stative-descriptive, and / or handling information.
These particles continue to decay, emitting alpha particles which can damage cells in the lung tissue.
These conditions can be used to handle unusual situations.
These antigens can sometimes be presented by tumor cells and never by the normal ones.
These can be as simple as a searchlight for a police helicopter or as complicated as the tactical system for an airborne early warning platform.

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