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Page "learned" ¶ 1165
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If and continuation
If in every situation only one transition is available as continuation of the computation, then the result is a deterministic pushdown automaton ( DPDA ), a strictly weaker device.
That means, define E ≤ F if E is an initial segment of F and the ordering of the members in E is the same as their ordering in F. If E is a chain in A, then the union of the sets in E can be ordered in a way that makes it a continuation of any set in E ; this ordering is a well ordering, and therefore, an upper bound of E in A.
If the continuation is never applied to an argument, the value of the expression is the same as the value of x.
If there are only small patches of cirrocumulus and perhaps some wisps of cirrus, it usually means a continuation of good weather and if it is seen after rain it usually means improving weather.
If he were to implant his Copy into the TVC universe, have the copy run a number of experiments to anchor itself in that universe, and then terminate it, only to find himself still in the TVC universe ( indeed, the purpose of growing the TVC universe from a Garden of Eden configuration was to prove to his Copy that such a TVC universe as it found itself to inhabit must have been launched from a non-TVC universe, as opposed to merely having always existed and evolved towards this the current state in which he did not know whether it had ) rather than back in " the real world " again, then he would be vindicated ; if not, then his hypothesis would be falsified and he might consider himself crazy ( his last several experiences of termination and subsequent continuation involved him finding himself in the position of having been recently cured of psychosis ).
If used to select candidates for an office, or for continuation to a next round of voting or play, it is either single-or multi-winner, as everyone who is not disapproved of is in effect a winner, for that round.
If this claim ( which Marx originally intended as a criticism of German Idealism and the more moderate Young Hegelians ) is still more or less the case in the 21st century, as many Marxists would claim, then Marxist theory is in fact the practical continuation of the philosophical tradition, while much of philosophy is still politically irrelevant.
If she no longer wanted to marry that man but instead wanted to marry the new tallest man in Fulsom County, and saw this as a continuation of her earlier desire, then she meant the original statement in a de dicto sense.
If elected Romney could severely impact the continuation of the project, set to begin building in 2013.
If it is played as a continuation of the first two modules, the players know that they are searching for the force behind the giant's alliance, otherwise they have been hired by nobles to destroy the fire giants.
If a wife were childless the husband often kept a concubine, whose offspring succeeded to the headship of the family, thus securing its continuation.

If and card
If the dealer's upcard is an ace, the player is offered the option of taking " insurance " before the dealer checks the hole card.
If there is a sense in which a card game can have an " official " set of rules, it is when that card game has an " official " governing body.
If it destroyed by another cards effect, you may add another " Nordic Relic " card to your hand.
If a player has three of a kind and several other players have drawn new cards, one strategy is to draw only one card.
If an unauthorized party obtains the card number in any way, a breach of confidentiality has occurred.
If we assemble a deck of 52 playing cards with no jokers, and draw a single card from the deck, then the sample space is a 52-element set, as each card is a possible outcome.
If the opponent is on a flush draw ( 9 / 46, approximately 19. 565 percent or 4. 11-to-1 odds against with one card to come ), the pot is not offering adequate pot odds for the opponent to call unless the opponent thinks he can induce additional final round betting from Bob if the opponent completes his flush draw ( see implied pot odds ).
* If splitting a pot because of tied hands, award the odd chip to the hand that contains the highest-ranking single card, using suits to break ties if necessary ( clubs ranking the lowest, followed by diamonds, hearts, and spades as in bridge ).
* If two cards are drawn with replacement from a deck of cards, the event of drawing a red card on the first trial and that of drawing a red card on the second trial are independent.
* If the notrump bidder bids 2, denying a 4-card major, responder may bid his 5 card major with a call of 2 of his major with 8-9 HCP, or with a call of 3 of his major with 10 HCP.
If not conducted properly, this method can be vulnerable to sensory leakage and card counting.
If the network interface is a plug-in card rather than being integrated into the motherboard, the card may need to be connected to the motherboard by an additional cable.
If either player turns up such a card, his opponent has to pay a penalty: four cards for an ace, three for a King, two for a Queen, or one for a Jack.
* If the two cards are of equal value, a third card is dealt.
If the third card is of the same value, then the payout for the player is 11: 1, otherwise the hand is a push.
* If neither of the above is the case ( for example, a three and an eight ), then a spread is announced which determines the payoff ( a 4-card spread, in this example ), and a third card will be dealt.
If the two cards played are of equal value, each player lays down three face-down cards and picks one of the cards out of the three ( a " war "), and the higher-valued card wins all of the cards on the table, which are then added to the bottom of the player's stack.
If a player runs out of cards while dealing the face-down cards of a war, he may play the last card in his deck as his face-up card and still have a chance to stay in the game.
If the player has no cards he can play, he must instead draw a new card from the top of the stack and, in some variants, say something such as " Pass ", " Penalty Card " or knock on the table to indicate inability to play a card.

If and follows
If we make it established custom that whenever butchery on the highways grows excessive, say beyond 25,000 per annum, then somebody is going to hang, it follows that the more eminent the victim, the more impressive the lesson.
If one follows the reports of the Congress, one finds that there still seems considerable uncertainty in the minds of the leaders themselves about what exactly to do in this matter.
If the Department of State is to take primary responsibility for foreign policy in Washington, it follows that the ambassador is expected to take charge overseas.
If **ya is the multiple secant of **zg which passes through Af and **yb is the simple secant of **zg which passes through Af, and if Af are the points in which **ya meets **zg, and if Af is the image of Af on the generator **yb, it follows that the image of the line Af is Af.
If the trend of general business activity follows the pattern suggested here, we are likely to see additional steps by the Federal Reserve authorities to ease the availability of credit.
If the defendant pleads guilty, an evidentiary hearing usually follows.
" If the tanks succeed, then victory follows ", he wrote.
If Chins Could Kill ... was published in 2002 and follows Campbell's career to date as an actor in low-budget films and television, providing his insight into " Blue-Collar Hollywood ".
If a bookmaker follows the rules of the Bayesian calculus in the construction of his odds, a Dutch book cannot be made.
From the criterion it also follows that Carmichael numbers are cyclic .< ref > Proof sketch: If is square-free but not cyclic, for two prime factors and of.
It follows that there are also infinitely many solutions if c is a multiple of the greatest common divisor of a and b. If c is not a multiple of the greatest common divisor of a and b, then the Diophantine equation ax + by = c has no solutions.
If one follows Polybius, the course of events was the following: Despite the Carthaginian pre-war naval advantage, the Roman landing was virtually unopposed.
In 1951, he summed up his vision as follows: " If the camera is to make a contribution at all to dance, this must be the focal point of its contribution ; the fluid background, giving each spectator an undistorted and altogether similar view of dancer and background.
If the arguments are both greater than zero then the algorithm can be written in more elementary terms as follows:
If X is a set with an equivalence relation denoted by infix, then a groupoid " representing " this equivalence relation can be formed as follows:
If the group G acts on the set X, then we can form the action groupoid representing this group action as follows:
If we define a function between these rings as follows:
If one follows broader linguistic tradition and counts singular and plural as belonging to the same class, then Swahili has 8 or 9 noun classes, Sotho has 11 and Ganda has 10.
If that plea is not guilty, a trial normally follows and the court gives the defendant the trial date at this arraignment.
If a point X is located on a parabola which has focal length and if is the perpendicular distance from X to the axis of symmetry of the parabola, then the lengths of arcs of the parabola which terminate at X can be calculated from and as follows, assuming they are all expressed in the same units.
If the negated query can be refuted, i. e., an instantiation for all free variables is found that makes the union of clauses and the singleton set consisting of the negated query false, it follows that the original query, with the found instantiation applied, is a logical consequence of the program.
If the negated query can be refuted, it follows that the query, with the appropriate variable bindings in place, is a logical consequence of the program.
If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.
* If baptism is a sign that a person is a member of God's covenant community, and if the children of believers are members of that community, it follows that the children of believers should receive the sign that they are members of God's covenant community by being baptized, as an infant is entitled to a passport that indicates the child as a member of a particular country.

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