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.

* In the Tales of Old Dartmoor episode ( recorded in 1956 ) of The Goons radio comedy series, Grytpype-Thynne arranges for the prison to put to sea to visit the Château d ' If in France as part of a plan to find the treasure of the Count of Monte Cristo hid there.

* If < math > a < b </ math > and < math > c < d </ math > then < math > a + c < b + d </ math >;

If R is a commutative ring, and a and b are in R, then an element d of R is called a common divisor of a and b if it divides both a and b ( that is, if there are elements x and y in R such that d · x = a and d · y = b ).

If d is a common divisor of a and b, and every common divisor of a and b divides d, then d is called a greatest common divisor of a and b.

If the target is a hard and heavy object, or if it is resting on some sort of anvil, the head can travel only a very short distance d before stopping.

If all contracts awarded reach their stated target plateau production then this will increase Iraqi production from today's 2. 5 mb / d by 9. 4 mb / d to a total of 11. 9 mb / d, comparable to current Saudi declared capacity of 12. 5 mb / d.

* We are allowed to " add inequalities ": If a ≤ b and c ≤ d, then a + c ≤ b + d

French-Canadian band Harmonium had a short career in the mid ' 70s during which their most notable release was Si on avait besoin d ' une cinquième saison ( If We Needed A Fifth Season ) ( 1975 ).

If X and Y are subsets of the real numbers, d < sub > 1 </ sub > and d < sub > 2 </ sub > can be the standard Euclidean norm, || · ||, yielding the definition: for all ε > 0 there exists a δ > 0 such that for all x, y ∈ X, | x − y | < δ implies | f ( x ) − f ( y )| < ε.

If we suppose the screen is far enough from the slits ( that is, s is large compared to the slit separation d ) then the paths are nearly parallel, and the path difference is simply d sin θ.

If scatterers are arranged symmetrically with a separation d, these spherical waves will be in sync ( add constructively ) only in directions where their path-length difference 2d sin θ equals an integer multiple of the wavelength λ.

If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If clay is slightly out of shape, square straight sides with guide sticks or rulers pressed against opposite sides, or smooth round pieces with damp fingers.

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 they don't then for the algorithm to be effective it must provide a set of rules for extracting a square root.

If it were square, would you make it round?

If the square mile is divided into quarters, each quarter has a side length of mile ( 880 yards ) and is square mile in area, or 160 acres.

Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

If F ( r ) represents gravity, it is a negative term proportional to 1 / r < sup > 2 </ sup >, so the net acceleration in r in the rotating frame depends on a difference of reciprocal square and reciprocal cube terms, which are in balance in a circular orbit but otherwise typically not.

If the mark is encountered again and the painter is traveling in the same direction, then the painter knows that it is safe to paint the square with the mark and to continue in the same direction.

If a player's piece lands on a square containing an opponent's piece, the opponent's piece is captured and returns to the starting area.

If the surface of concentric sphere shells were considered, the number of stars on each shell would be proportional to the square of the radius of the shell.

If E < sub > i </ sub > is a sine wave, triangular wave, or wave of any other shape that is symmetrical around zero, the zero-crossing detector's output will be square.

The algorithm for deciding this is conceptually simple: it constructs ( the description of ) a new program t taking an argument n which ( 1 ) first executes program a on input i ( both a and i being hard-coded into the definition of t ), and ( 2 ) then returns the square of n. If a ( i ) runs forever, then t will never get to step ( 2 ), regardless of n. Then clearly, t is a function for computing squares if and only if step ( 1 ) terminates.

If either the 2nd player chooses to move to the square diagonal to the first player or the first player's 2nd move is not to this square given the choice, then a starting position before flipping moves commence that differs from the standard Othello position arises.

If this is around 1 the engine is said to be " square ", if it is greater than 1, i. e. the bore is larger than the stroke, it is " oversquare ".

If the quantity under the square root ( the discriminant ) is negative, then the ray does not intersect the sphere.

* If A is a square matrix ( i. e., m = n ), then A is invertible if and only if A has rank n ( that is, A has full rank ).

If the material superconducts in the absence of a field, then the superconducting phase free energy is lower than that of the normal phase and so for some finite value of the magnetic field ( proportional to the square root of the difference of the free energies at zero magnetic field ) the two free energies will be equal and a phase transition to the normal phase will occur.

( If one of the basic hand-shape glyphs is used, such as the simple square or circle, this band breaks it in two ; however, if there are lines for fingers extended from the base, then they become detached from the base, but the base itself remains intact.

If a piece falls into the center square, the game is over.

* If a piece is pushed right next to the center square, it immediately disappears.

If the strategy ever called for moving on the square already chosen, the first player can then make another arbitrary move.

If, on completion of a move, a player's token lands on the lower-numbered end of a " ladder ", the player moves his token up to the ladder's higher-numbered square.

If he lands on the higher-numbered square of a " snake " ( or chute ), he must move his token down to the snake's lower-numbered square.