21 The proposed DSM-5 criteria have resulted in vociferous criticism, 2, 15, 22, 23 mostly because of their implication that there exists such a "thing" as a unique and narrow phenotype of autism.
For the converse implication, suppose that there exists x ∈ C such that the sequence { T n x } n ∈ N is bounded.
Moreover, McCall points out that CC1 has some properties that are difficult to justify if the name 'connexive logic' is meant to reflect the fact that in a valid implication A→ B there exists some form of connection between the antecedent A and the succedent B. Axiom A4, for example, is bad in this respect.
For the converse implication, suppose that there exists a bounded sequence { x n } n ∈ N in C such that lim inf n → ∞ ∥ x n − T x n ∥ = 0. Consequently, there is a bounded subsequence { T x n k } k ∈ N of { T x n } n ∈ N such that lim k → ∞ ∥ T x n k − x n k ∥ = 0. Suppose A ( C, { x n k } k ∈ N ) = { z }.
The following three examples tell us that for each implication except (Cont → Bro), there exists a counterexample for its converse implication.
A function I L×L→L is called a QL-implication if there exist a t-norm T, a t-conorm S and a fuzzy negation N such that I x,y) = S(N x ,T x,y)) (4).
Hence, for any (varepsilon_{3}in 0,1/2]), there exists (varepsilon_{4}in 0,varepsuchn_{3}/2]) such that the first implication in claim 3 is satisfied for any (pinDelta ^{n}): (p_{n}leq1-varepsilon_{3}).
Hence, there exists (varepsilon_{1}in 0,1/2]) such that the considered implication is satisfied.
If the forecasted exposure level is greater than the threshold dose, i.e. HQ > 100%, there exists potential risks of adverse human health implications for the particular NM.
"Nothing out there exists".
