Now it is easy to convince oneself that the set X could not possibly be measurable for any rotation-invariant countably additive finite measure on S. Hence one couldn't expect to find an algorithm to find a point in each orbit, without using the axiom of choice.

The difficulty is heightened when songs merge, as in " Now "/" Later "/" Soon ", because all three have to be performed in the same key, limiting the ability to pick a comfortable key for each singer.

Now setting all of the X < sub > s </ sub > equal to the unlabeled variable X, so that the product becomes, the term for each k-combination from S becomes X < sup > k </ sup >, so that the coefficient of that power in the result equals the number of such k-combinations.

Now, due to physical properties of interference, if two signals at a point are in phase, they add to give twice the amplitude of each signal, but if they are out of phase, they subtract and give a signal that is the difference of the amplitudes.

Now there are two related linear equations, each with two unknowns, which lets us produce a linear equation with just one variable, by subtracting one from the other ( called the elimination method ):

Now, let us say that the purpose is not legal entitlement, but rather, the following situation: The admiral of the fleet believes that captains and crews who have fought alongside each other are more effective than captains and crews who are strangers to each other.

By the Chinese Remainder Theorem, this ring factors into the direct product of rings of integers mod p. Now each of these factors is a field, so it is clear that the only idempotents will be 0 and 1.

Now Olga gave to each soldier in her army a pigeon or a sparrow, and ordered them to attach by thread to each pigeon and sparrow a piece of sulfur bound with small pieces of cloth.

As a result, various other companies control the international distribution rights to Apocalypse Now ( in some countries, each version has a different distributor ).

Now choose any consumer purchasing both goods, and measure his utility in such units that in equilibrium his marginal utility of money ( the increase in utility due to the last unit of money spent on each good ), MU < sub > 1 </ sub >/ p < sub > 1 </ sub >= MU < sub > 2 </ sub >/ p < sub > 2 </ sub >, is 1.

Now the cohorts were ten permanent units, composed of 6 centuries and in the case of the first cohort 12 centuries each led by a centurion assisted by an optio.

Now, each is obviously a vector in the column space of.

Now each province is administered by a directly elected provincial council:

Some see an internal contradiction between the mention already in Genesis 10: 5 that " From these the maritime peoples spread out into their territories by their clans within their nations, each with his own language " and the subsequent Babel story, which begins " Now the entire earth was of one language and uniform words " ( Genesis 11: 1 ).

Now, if both twins send a video feed of themselves to each other, what do they see in their screens?

Now imagine that you wish to perform some process on each of these digits, for example, adding the number two to each digit.

Now they consist of several redundant multi-gigabyte SCSI drives that each reside on a card.

Now both armies began firing arrows at each other.

Now, form a sequence by performing this operation repeatedly, beginning with any positive integer, and taking the result at each step as the input at the next.

Now each alderman must submit himself for re-election at least once in every six years.

Now for a given disposition of the antennas, the reciprocity theorem requires that the power transfer is equally effective in each direction, i. e.

Now, for each block B < sub > 1 </ sub > of 4x4 pixels in A < sub > 1 </ sub >, find the corresponding block B < sub > 2 </ sub > in A < sub > 2 </ sub > most similar to B < sub > 1 </ sub >, and then find the grayscale or RGB offset and gain from A < sub > 2 </ sub > to B < sub > 2 </ sub >.

Now good definition is one thing that all of us can acquire with occasional high-set, high-rep, light-weight workouts.

Now the thing for us to do is to find ourselves a couple of those wonderful flowering currants such as the red Ribes sanguineum of our Pacific Northwest, or otherwise a good sloe tree, or perhaps some nice pussy willow in bloom, preferably one with male or staminate catkins.

Instead, the philosopher encounters a problem :" Now, if the ' to be ' of a thing could be conceived apart from that which exists, it should be represented in our mind by some note distinct from the concept of the thing itself ....

Pale, lifeless face, tired painful eyes, and only speaking about the same thing: ' Now it all doesn ’ t matter, I declined the Prize.

The Russian stated: "' Now, if he does not say the right thing to them we are all done for '"-On the stretcher Marlow could see Kurtz shouting.

“ Now let us understand the exact meaning of the expression historical Judaism … Looking at Judaism from a historical point of view, we become convinced that there is no one aspect deep enough to exhaust the content of such a complex phenomenon as Judaism … Accordingly, Torah-less Judaism … would be an entirely new thing and not the continuation of something given …

Now, recall that a universal, like greenness, is supposed to be a single thing.

Now ... the play was the thing, and everything else was subservient to that play.

In a footnote to the preface of Blaze, dated 30 January 2007, King wrote of Rage: " Now out of print, and a good thing.

Now, the next big thing being worked on is an astonishingly accurate version of the mythic Spa Francorchamps Belgian track with its 1967 sixties layout. Originally, the track included in the game, suffered some unaccuracies. Spa 67 release is expected for 2012.

Now one of these ambassadors from the people of Alexandria was Apion, ( 29 ) who uttered many blasphemies against the Jews ; and, among other things that he said, he charged them with neglecting the honors that belonged to Caesar ; for that while all who were subject to the Roman empire built altars and temples to Gaius, and in other regards universally received him as they received the gods, these Jews alone thought it a dishonorable thing for them to erect statues in honor of him, as well as to swear by his name.

Now he presents his Problemata ( problems ): " Abraham has gained a prescriptive right to be a great man, so that what he does is great and when another does the same thing it is a sin.

Now with Shima Katase looking like she would surpass Ayaka as well, the same thing almost happened.

In Joshua Then and Now by Mordecai Richler, the title character's father Reuben Shapiro has a unique understanding of the bible based upon his days as a prize-fighter, when the only thing to do in the hotel room was read Gideon's Bible.

He was in fact denounced as a sexually ambiguous figure in his time most notably by William Pulteney, then leader of the Opposition and as cited above, by Alexander Pope in his " Sporus " portrait: " Let Sporus tremble / What that thing of silk ... His wit all seesaw between that and this / Now high, now low, now master up, now miss / And he himself one vile antitheseis ...".

When later questioned, Krenwinkel claimed that the only thing going through her mind at the time was that " Now he won't be sending any of his children off to war.

In a footnote to the preface of Blaze ( dated 30 January 2007 ) King wrote of Rage: " Now out of print, and a good thing.

*" Now, there's a funny thing "

In a footnote to the preface of the more recent Bachman book Blaze ( dated 30 January 2007 ) King wrote of Rage: " Now out of print, and a good thing.

*" Now, that's the thing aboot debt.

Ed Sullivan: " Now, what do you consider the most important thing in rocket travel?

Now a thing is not declared to be soft through yielding to a heavy blow, for walls yield to the battering-ram.

Now you can feel the power without touching a thing.