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If and number
If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.
If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.
If a nation wished to get a head start in physical fitness over all other nations, it would start its kindergarten students on a program of gymnastics the day they entered and thus eliminate a large number of the problems that plague American schools.
If no specific organization plan exists limiting the number of scientists at each salary level, the result is a department top-heavy with high-level, high-salaried personnel ''.
If we thus spent our very first day in the midst of a large number of your people honoring a new hero and a great national achievement, our last day, to us at least, was equally impressive and very moving, even though the crowds were absent and there was almost complete silence.
If a wedge-shaped coating of increasing thickness is removed from a substrate by an instrument like the Hesiometer with a knife of constant rake angle, a number of removal mechanisms are often observed which depend upon the thickness of the coating.
If all the operating variables were varied simultaneously, Af operations would be required to do the same job, and as R increases this increases very much more rapidly than the number of operations required by the dynamic program.
If Rock shows up during the number -- or you hear anything -- give me the signal ''.
If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.
If so, it might be worth while to assign a future jazz show to a different department -- one with enough confidence in the musical material to cut down on the number of performers and give them a little room to display their talents.
* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.
If its minimal polynomial has degree, then the algebraic number is said to be of degree.
If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.
* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )
If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).
If a ) testimonies conflict one another, b ) there are a small number of witnesses, c ) the speaker has no integrity, d ) the speaker is overly hesitant or bold, or e ) the speaker is known to have motives for lying, then the epistemologist has reason to be skeptical of the speaker's claims.
If we take in our hand any volume ; of divinity or school metaphysics, for instance ; let us ask, Does it contain any abstract reasoning concerning quantity or number?
If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.
If the two carbon atoms at the double bond are linked to a different number of hydrogen atoms, the halogen is found preferentially at the carbon with fewer hydrogen substituents ( Markovnikov's rule ).
If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.
If there is no number to its left, simply look at the column headed " 1 " in the previous row.
If the game has been scored correctly, the total number of plate appearances for a team should equal the total of that team's runs, men left on base, and men put out.
If the other player also knows to offer sacrifices, the expert also has to manipulate the number of available sacrifices through earlier play.

If and counts
If one player has not borne off any checkers by the time that player's opponent has borne off all fifteen, then the player has lost a gammon, which counts for double a normal loss.
If the losing player has not borne off any checkers and still has checkers on the bar or in the opponent's home board, then the player has lost a backgammon, which counts for triple a normal loss.
If this output is then used as the clock signal for a similarly arranged D flip-flop ( remembering to invert the output to the input ), you will get another 1 bit counter that counts half as fast.
If the feature vectors include features of many different kinds ( discrete, discrete ordered, counts, continuous values ), some algorithms are easier to apply than others.
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 rotations are also considered distinct, then the pentominoes from the first category count eightfold, the ones from the next three categories ( T, U, V, W, Z ) count fourfold, I counts twice, and X counts only once.
If the opponent in the hold begins to tap out at the same time a referee counts to three for pinning the opponent delivering the hold, both opponents have legally achieved scoring conditions simultaneously.
* If the word ends in a consonant cluster, only the final consonant counts.
If they have less, it counts as a fair shot.
If all are unique, then counts the number of unique values, and counts the number of samples.
If two are playing, then each player counts out 40 infantry, plus 40 more from a different color set.
If three are playing, each player counts out 35 infantry ; four players, 30 infantry ; five players, 25 infantry ; six players, 20 infantry.
If the signal data are not constant, then can be calculated from data where the signal is zero or relatively constant .</ ref > Notice that such an alternative definition is only useful for variables that are always non-negative ( such as photon counts and luminance ).
If one counts in Gray code of a bit size equal to the number of disks in a particular Tower of Hanoi, begins at zero, and counts up, then the bit changed each move corresponds to the disk to move, where the least-significant-bit is the smallest disk and the most-significant-bit is the largest.
If Yoshi is struck by an enemy or obstacle, Baby Mario will be sprung from Yoshi's back and float around in a bubble crying while a timer counts down, requiring Yoshi to try and recover him by popping its bubble.
* If the non-dealer asks for fewer cards than he has discarded, the dealer counts as tricks all cards which cannot be played to.
If the dealer play with fewer than five cards, the non-dealer counts as tricks all cards which cannot be played to.
If a team hits a ' six and out ' to win the game, the team wins and the batsman goes out, plus the six counts, whatever the set amount of wickets may be ( even if the wicket was the teams ' last ).
If a player rolls doubles, each die still counts only once.
If we determine the number of hands that contain two red cards, by symmetry relations we will necessarily also know the hypergeometric distributions governing the other three quadrants: hand counts for red / black, black / red, and black / black.
If one counts from the beginning of AD 1 to the ending of AD 1000, one would have counted 1000 years.

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