Some articles on implies:

Four Exponentials Conjecture - Corollaries
... Using Euler's identity this conjecture implies the transcendence of many numbers involving e and π. 2, y1 = iπ, and y2 = iπ√2, the conjecture — if true — implies that one of the following four numbers is transcendental The first of these is just −1, and the fourth is 1, so the ... By setting x1 = 1, x2 = t, y1 = log2, and y2 = log3, the four exponentials conjecture implies that if t is irrational then one of the following four ...
Suslin Tree
... The diamond principle, a consequence of V=L, implies that there is a Suslin tree, and Martin's axiom MA(ℵ1) implies that there are no Suslin trees ... Whether the Generalized Continuum Hypothesis implies the existence of an ℵ2-Suslin tree, is a longstanding open problem ...
Continuous Stochastic Process - Relationships
... In particular continuity with probability one implies continuity in probability continuity in mean-square implies continuity in probability continuity with probability one neither implies ...
Tautology (logic) - Definition and Examples
... ("if A implies B then not-B implies not-A", and vice versa), which expresses the law of contraposition ... ("if not-A implies both B and its negation not-B, then not-A must be false, then A must be true"), which is the principle known as reductio ad absurdum ... ("if A implies B and B implies C, then A implies C"), which is the principle known as syllogism ...
Causal Structure - Introduction - Causal Relations
... These relations are transitive , implies , implies and satisfy implies (this follows trivially from the definition) , implies , implies ...

Famous quotes containing the word implies:

    Lovers have a way of using this word “nothing” which implies exactly the opposite.
    Honoré De Balzac (1799–1850)

    I’m a priest, not a priestess.... “Priestess” implies mumbo jumbo and all sorts of pagan goings-on. Those who oppose us would love to call us priestesses. They can call us all the names in the world—it’s better than being invisible.
    Carter Heyward (b. 1946)

    Religion means goal and way, politics implies end and means. The political end is recognizable by the fact that it may be attained—in success—and its attainment is historically recorded. The religious goal remains, even in man’s highest experiences, that which simply provides direction on the mortal way; it never enters into historical consummation.
    Martin Buber (1878–1965)