Sentence examples for a implies from inspiring English sources

Brouwer remarks in the 1908 paper that the fact that PEM is not valid does not mean that it is false: ¬(A ∨ ¬ A) implies ¬A ∧ ¬¬A, a contradiction.

end{aligned} Moreover, (Gin B({x},varepsilon capkappa(A)) implies (Gsubseteq B x,varepsilon)) and (Gsubseteq A), consequently, (y_{0}in B x,varepsilon cap A).

Second, because Spanish debt is in euros, scenario A implies a significantly worse debt burden.

Obviously, (a) implies (b).

Thus (a) implies (b).

Proof (a) implies (b).

Then, (i) (A) implies (B).

which together with (a) implies (3.14).

Since ∑ a n is summable | A | implies ∑ a n λ n is summable | B | k, by the hypothesis of the theorem, ∥ X ∥ < ∞ ⇒ ∥ Y ∥ < ∞.

end{aligned} end{aligned} Note that (h < frac{{a - b}}{a}) implies (a-b-ax) stays positive on the interval ([ 1-p h,h]).

Furthermore, condition (thetain s a,A)) implies (ain A) for all (ain X) and (Asubseteq X), even though A is not closed.