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Now we define an ordering of the k-tuples of natural numbers as follows: < math > ( x_1 ... x_k ) < ( y_1 ... y_k ) </ math > should hold if either < math >
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Now and we
Now, roaring up in great oily clouds of smoke and flames, the fierce heat quickly drove us to the stern where we huddled like suffocating sheep, not knowing what to do.
Now we peered anxiously for any speck of land in the Pacific, for this interminable bailing would have to stop soon.
Now in the mere fact of the beginning of such displacement we have prima-facie evidence of the ontological weakness of the fading form.
Now we can argue that the irresistible fate of Oedipus Rex was nothing more than the irresistible unconscious longings of Oedipus projected outward, but this externalization of unconscious conflict makes all the difference between a story and a clinical case history.
Now omitting for a moment some recent developments we can say the Saxon Shore hypothesis of Lappenberg and Kemble has undergone virtual eclipse in this century.
Now Hans had given Ma something of his -- we both had when we thought she was going straight to Pa -- something valuable ; ;
Now place 12 pieces 1/2'' '' sq. on this edge as we did before and space them with the 5-3/4'' '' long `` tappets '', as they are called.
Now, to add to the already unbelievable extremes found in one nation, we have the two new states of Hawaii and Alaska.
Now Rangoni comes to the point, and we hear, for the first time, a long, downward chromatic scale that will become the characteristic motif of his sinister power.
Now we might have restricted the use of uranium bombs by controlling the sources of uranium because it is found in only a few places in the world.
For Queen Anne also, the Ramillies campaign had one overriding significance – " Now we have God be thanked so hopeful a prospect of peace.
Now, men, Sinn Fein have had all the sport up to the present, and we are going to have the sport now.
Now and define
Now, taking this derived formula, we can use Euler's formula to define the logarithm of a complex number.
Now we define a new property G: if x is an object in some possible world, then G ( x ) is true if and only if P ( x ) is true in that same world for all positive properties P. G is called the " God-like " property.
Now define by transfinite induction a sequence G < sup > m </ sup >, where m is an ordinal number, in the following manner:
Now we can define division of formal power series by defining B / A to be the product B A < sup > − 1 </ sup >, provided that the inverse of A exists.
Now, if we're given a vector field Y over M ( but not the principal bundle ) but we also have a connection over the principal bundle, we can define a vector field X over the principal bundle such that its horizontal component matches Y and its vertical component agrees with the connection.
Since S is non-empty, there is a rational number L such that L < s for some s in S. Now define sequences of rationals ( u < sub > n </ sub >) and ( l < sub > n </ sub >) as follows:
Again, because of linearity, this suffices to define Δ and ε uniquely on all of K. Now K is both a unital associative algebra and a coalgebra, and the two structures are compatible.
Now we can define the dominance frontier: a node B is in the dominance frontier of a node A if A does not strictly dominate B, but does dominate some immediate predecessor of B ( possibly node A is the immediate predecessor of B.
Now one can go even further and define orders where arbitrary joins distribute over arbitrary meets.
Now, we define two kinds of creation / destruction operators, acting on different Hilbert spaces ( initial space i, final space f ), and.
Now, we define the coordinate vector of v relative to B to be the following sequence of coordinates:
2.923 seconds.