Then, on July 2, there occurred another incident which set tongues to wagging at a furious clip.

Then O'Banion was presented with a platinum watch set with rubies and diamonds.

`` Then maybe it was the shockwave we set up.

Then our choice function can choose the least element of every set under our unusual ordering.

Then, taking in on the first cable as the boat is motored into the wind and letting slack while drifting back, a second anchor is set approximately a half-scope away from the first on a line perpendicular to the wind.

Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies.

Then codenamed " Stella ," the machine was also set to utilize cartridges ; after seeing the Channel F, Atari realized they needed to release it before the market was flooded with cartridge-based machines.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Then Asmund set himself to wait the agreed upon three days:

Then the Cartesian product set D < sub > 1 </ sub > D < sub > 2 </ sub > can be made into a directed set by defining ( n < sub > 1 </ sub >, n < sub > 2 </ sub >) ≤ ( m < sub > 1 </ sub >, m < sub > 2 </ sub >) if and only if n < sub > 1 </ sub > ≤ m < sub > 1 </ sub > and n < sub > 2 </ sub > ≤ m < sub > 2 </ sub >.

Let G be a set and let "~" denote an equivalence relation over G. Then we can form a groupoid representing this equivalence relation as follows.

Then the equivalence class of the pair can be identified with the rational number, and this equivalence relation and its equivalence classes can be used to give a formal definition of the set of rational numbers.

Then an " estimator " is a function that maps the sample space to a set of sample estimates.

Then, in the grand final against Melbourne, Essendon set a grand final record score of 22. 18 ( 150 ) to Melbourne 13. 9 ( 87 ), with 7 goal centre half forward Gordon Lane.

Then one " flows " the charge by systematically redistributing the charge from a vertex to its neighboring vertices according to a set of rules, the discharging procedure.

is partially ordered by set inclusion, therefore it contains a maximal totally ordered subset P. Then the set satisfies the desired properties.

Then the image set f ( I ) is also an interval, and either it contains f ( b ), or it contains f ( a ); that is,

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

Then Lothair finally set out with a large Lombard army, but Louis had promised his sons Louis the German and Pepin of Aquitaine greater shares of the inheritance, prompting them to shift loyalties in favour of their father.

Then worship Allah and do not associate anything with Him, perform the Hajj and the ‘ Umrah, be righteous, and all affairs will be set right for you.

Then the null set automatically has measure zero because of countable additivity, because and is finite if and only if the empty set has measure zero.

Then N < sub > x </ sub > is a directed set, where the direction is given by reverse inclusion, so that S ≥ T if and only if S is contained in T. For S in N < sub > x </ sub >, let x < sub > S </ sub > be a point in S. Then ( x < sub > S </ sub >) is a net.

Then x is a rational number greater than 0 and less than r < sub > 0 </ sub >.

Then, these philosophers say, it is rational to act on those beliefs that have best withstood criticism, whether or not they meet any specific criterion of truth.

Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

Then every Hodge class on X is a linear combination with rational coefficients of Chern classes of vector bundles on X.

Then every Hodge class on X is a linear combination with rational coefficients of Chern classes of coherent sheaves on X.

Then all vanish for sufficiently large n. One can then show for some polynomial P over rational numbers.

Then Z ( s ), according to our definition, is well-defined only up to multiplication by rational functions in a finite number of.

Then, since is assumed rational, there must exist, positive integers such that

Then, in the safe refuge of Rome, he raised his voice for the relief of the oppressed, in numerous writings in which he characterized the Holy Office of Portugal as a tribunal which served only to deprive men of their fortunes, their honor and their lives, while unable to discriminate between guilt and innocence ; it was known to be holy only in name, while its works were cruelty and injustice, unworthy of rational beings, although it was always proclaiming its superior piety.

Then you figure out what desires it ought to have, on the same considerations, and finally you predict that this rational agent will act to further its goals in the light of its beliefs.

Then there exists an r-tuple of rational numbers ( a < sub > 1 </ sub >,..., a < sub > r </ sub >) such that

Then A is dense in C ( X, R ) if and only if it separates points.

Then they come up with 24 unanswered points.

Then during the regular-season finale on December 17, 1983, Moseley set an NFL scoring record with 161 points while Riggins ' total of 144 points was second.

Then the nerve layers identify simple shapes, such as bright points surrounded by dark points, edges, and movement.

Then the raw mark is subtracted from the maximum points possible.

Then two points x and y in X are topologically distinguishable if they do not have exactly the same neighbourhoods ( or equivalently the same open neighbourhoods ); that is, at least one of them has a neighbourhood that is not a neighbourhood of the other ( or equivalently there is an open set that one point belongs to but the other point does not ).

Then, applying transformation T to all the points on this sphere yields

In particular, let p define the coordinates of points in a reference frame M coincident with a fixed frame F. Then, when the origin of M is displaced by the translation vector d relative to the origin of F and rotated by the angle φ relative to the x-axis of F, the new coordinates in F of points in M are given by

Examples: William Faulkner in A Rose for Emily ( Faulkner was an avid experimenter in using unusual points of view-see his Spotted Horses, told in third person plural ); Frank B. Gilbreth and Ernestine Gilbreth Carey in Cheaper By the Dozen ; Frederik Pohl in Man Plus ; and more recently, Jeffrey Eugenides in his novel The Virgin Suicides and Joshua Ferris in Then We Came to the End.

Then the total number of intersection points of X and Y with coordinates in an algebraically closed field E which contains F, counted with their multiplicities, is equal to the product of the degrees of X and Y.

Then, ten tricks are played, allowing players to take trick points: each card has a face value ( except in Null games ) and is worth that amount in points for the player winning the trick.

Then the set of fixed points of f in L is also a complete lattice.

Then the centroid of the figure is the weighted average of the three points.

Then the real Chippy Crescent wrapped the defeated team up in bandages, so they couldn't move, making them lose, although only by two points.

Then, the listing is simply " cut " at each of these points, and basic blocks remain.

Then it also has its extreme northern and southern azimuth points of rising and setting on the horizon ; its extreme lowest and highest altitude when crossing the meridian ; and potentially extreme late first sightings of the new moon.

Then letting ψ < sub > β </ sub >( λ ) be the λ < sup > th </ sup > β-inaccessible cardinal, the fixed points of ψ < sub > β </ sub > are the ( β + 1 )- inaccessible cardinals ( the values ψ < sub > β + 1 </ sub >( λ )).

Then Newton's diagram has points at ( 3, 0 ), ( 1, 1 ), and ( 0, 3 ).

Then, there are 15 points, and there are also 7 starting lines on each point.

While enumerating the high points of British cuisine, he touches on Stilton: " Then there are the English cheeses.