Since the set of complex numbers with " ? " 2 1 } } form the unit circle in the complex plane, it follows that for each point in, the inverse image is a circle, i . e .,.
42.
Given a homomorphism f : S \ to L from an arbitrary semigroup to a semilattice, each inverse image S _ a = f ^ {-1 } \ { a \ } is a ( possibly empty ) semigroup.
43.
In other words : The essential range of a complex-valued function is the set of all complex numbers " z " such that the inverse image of each ?-neighbourhood of " z " under " f " has positive measure.
44.
Also, the two inverse images of c under the doubling map ( \ frac { \ theta _ c } 2 and \ frac { \ theta _ c + 1 } 2 ) are both in every critical arc.
45.
(Instead of relations depending on unknowns, one should speak more correctly of predicates, the collection " E " is their logical conjunction, and the solution set is the inverse image of the boolean value " true " by the associated boolean-valued function .)
46.
The adjointness condition makes " g " the inverse image function " f " " 1, while the choice of " X " for the codomain of " g " corresponds to the requirement for continuous functions that the inverse image of open sets be open.
47.
The adjointness condition makes " g " the inverse image function " f " " 1, while the choice of " X " for the codomain of " g " corresponds to the requirement for continuous functions that the inverse image of open sets be open.
48.
It receded by 0.1 percent in the first three months of 1993, when a snapshot of the economy would have produced an inverse image of today's _ companies were expanding investment in technological equipment, consumers were reducing their spending and there was a sharp decline in military spending.
49.
The term " indefinite summation " refers to the search for an inverse image of a given infinite sequence " s " of values for the forward difference operator, in other words for a sequence, called antidifference of " s ", whose finite differences are given by " s ".
50.
It receded by 0 . 1 percent in the first three months of 1993, when a snapshot of the economy would have produced an inverse image of today's _ companies were expanding investment in technological equipment, consumers were reducing their spending and there was a sharp decline in military spending.
