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A life insurance trust is an irrevocable, non-amendable trust which is both the owner and beneficiary of one or more life insurance policies. [1] Upon the death of the insured, the trustee invests the insurance proceeds and administers the trust for one or more beneficiaries.
This definition makes the concept of proof amenable to study. Indeed, the field of proof theory studies formal proofs and their properties, the most famous and surprising being that almost all axiomatic systems can generate certain undecidable statements not provable within the system. The definition of a formal proof is intended to capture the ...
Actuarial science became a formal mathematical discipline in the late 17th century with the increased demand for long-term insurance coverage such as burial, life insurance, and annuities. These long term coverages required that money be set aside to pay future benefits, such as annuity and death benefits many years into the future.
Testability is a primary aspect of science [1] and the scientific method. There are two components to testability: Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logically possible. The practical feasibility of observing a reproducible series of such counterexamples if they do exist.
For Nature, or more precisely experiment, is an inexorable and not very friendly judge of his work. It never says "Yes" to a theory. In the most favorable cases it says "Maybe", and in the great majority of cases simply "No". If an experiment agrees with a theory it means for the latter "Maybe", and if it does not agree it means "No".
An immediate corollary of Löb's theorem is that, if P is not provable in PA, then "if P is provable in PA, then P is true" is not provable in PA. Given we know PA is consistent (but PA does not know PA is consistent), here are some simple examples: