In fact it appears that the simplest proof for this problem involves an induction where you assume the statement for a string whose length is TWO less than the string you need to prove something about.
To prove the result, let us assume the statement to be false, then there exist two constants (T>0) and (epsilon in (0,1)) such that begin{aligned} P{tau _{infty }leq T}>epsilon, end{aligned} (3.2) thus there exists an integer (r_{1} geq r_{0}) such that begin{aligned} P{tau _{r}leq T}geq epsilon, end{aligned} (3.3) for all (r geq r_{1}).
Rather than assuming that the statement was intended to be insulting, give the benefit of the doubt, and allow for some ignorance on the part of the speaker.
To this end, assume the contrary statement that ∑ ℓ = n ∞ ω ( ℓ + 1 ) ω = ∞.
Finally, the axiom of Foundation is equivalent, assuming the other axioms, to the statement that every set belongs to some $V_\alpha$, for some ordinal $\alpha$.
There was broad agreement that the core benefit of an assurance statement - assuming the provider has credibility - relates to internal leverage.
Instead, I simply assess them on the basis of the available information upon which, I assume, the various statements are based.
The network model used in the simulations assumes the following statements.
Nothing was mentioned about child benefit in the autumn statement, but assuming the provisions of the Uprating bill are applied to child benefit from April next year, expect another 20p for the first child and 15p for the second.
The purchase price represents a $750 million premium to the total worth of the assumed operations, the statement said.
