use axiom in a sentence
1) Then use all three axioms of a stochastic set.
2) Gudykunst uses 47 axioms as building blocks for the theorems of AUM.
axiom collocations
3) If these axioms are used, then some of the above might become theorems.
4) This system resists change and it can be hard to actively use the five axioms.
use axiom example sentences
5) The pieces in this decomposition, constructed using the axiom of choice, are non-measurable sets.6) Using the axiom of choice, they select and memorize a representative sequence from each equivalence class.
7) The arithmetical operations of addition and multiplication and the order relation can also be defined using first-order axioms.
8) Weil's proof used the axiom of choice and Henri Cartan furnished a proof which avoided its use.
9) Synthetic Spacetime, a digest of the axioms used, and theorems proved, by Wilson and Lewis.
10) The first four groups of axioms of Hilbert's axioms for plane geometry can be proved using Tarski's axioms.
11) The respective functions and relations are constructed in second-order logic, and are shown to be unique using the Peano axioms.
12) AD is provably false from ZFC; using the axiom of choice one may prove the existence of a non-determined game.
13) It is known that any filter can be extended to an ultrafilter, but the proof uses the axiom of choice.
14) Gödel and Paul Cohen showed that this hypothesis cannot be proved or disproved using the standard axioms of set theory.
example sentences with axiom
15) In order to better explain sojourners' cross-cultural adaptation, axioms are used to express causal, correlational, or teleological relationships.16) This contrasts with the axiomatic systems which instead use axioms as much as possible to express the logical laws of deductive reasoning.
17) Clavius, for example, was happy to accept the Copernican model as a mathematical model, but he declared that Copernicus had saved the appearances by using axioms which were physically false.
18) It is known to be neither provable nor refutable using the axioms of Zermelo–Fraenkel set theory, the standard foundation of modern mathematics, provided ZF set theory is consistent.
19) While in Euclid's time magnitudes were viewed as line segments and then results were deduced using the axioms or theorems of geometry.
20) If Γ is a set of formulas and "A" a formula, then __FORMULA__ means that "A" is derivable using the axioms and rules above and formulas from Γ as additional hypotheses.
21) MK was first set out in and popularized in an appendix to J. L. Kelley's (1955) "General Topology", using the axioms given in the next section.
22) The QPR team contained Vinnie Jones, who had a violent reputation and played using the axiom "if their top geezer gets sorted out early doors, you win".
23) The proof that "M"∗ is (usually) not the same as "M" is nonconstructive and uses the axiom of choice in an essential way; it is very hard to exhibit explicit elements of "M" that are not in "M"∗.
24) The method of constructing infinitesimals of the kind used in nonstandard analysis depends on the model and which collection of axioms are used .
25) Montague (1961) included a result first proved in his 1957 Ph.D. thesis: if ZFC is consistent, it is impossible to axiomatize ZFC using only finitely many axioms.
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