If the separation, power set and choice principles are axioms, then for a given M in the domain, there will be choice functions/sets on the subsets of M, consequently well-orderings, and so forth; if these principles are not included as axioms, then such demonstrations of existence will not be forthcoming.
The study presents a rigorous mathematical demonstration of existence and uniqueness of the solution of well-posed dynamic elastoplasticity problems.
Theorem 1.2 is particularly useful in the demonstration of existence and uniqueness of solutions to certain problems in analysis and economics (see [4 6]).
Demonstration of existence, timing, and duration of target pathophysiology affected by candidate intervention in human disease (proof of mechanism).
This result is fully consistent with our earlier demonstration of existence of heme bL– bL electron transfer reported for cross-inactivated WB BN constructed using the caps caps fusion system [10].
The Five Ways, Latin Quinquae Viae, in the philosophy of religion, the five arguments proposed by St. Thomas Aquinas (1224/25 1274) as demonstrations of the existence of God.
In 1938 Fermi received the Nobel Prize in Physics at the age of 37 for his "demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons".
Although by 1938 some scientists, including Niels Bohr, were still reluctant to accept that Fermi had actually produced a new element, he was nevertheless awarded the Nobel Prize in Physics in November 1938 "for his demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons".
Using the p-value as a criterion, the most convincing demonstrations of the existence of correlations appear in the most abundant proteins of the vacuolar membrane and cell periphery.
In the 1950s, Deome and colleagues [ 20] performed one of the earliest demonstrations of the existence of adult mammary stem cells, using a limiting-dilution assay showing that clonal precursor cells are capable of forming functional mammary outgrowths in a murine transplantation model.
Clearly, everything here depends on what is to count as 'external', in particular whether Moore's demonstration of the existence of his hands proves the existence of things that are in no way at all dependent upon experience or thought.
