If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

If this limit fails to exist then there is no oblique asymptote in that direction, even should the limit defining m exist.

If a detector was placed at a distance of 1 m, the ion flight times would be X and Y ns.

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 ( m, n ) is regular and M and N have i and j prime factors respectively, then ( m, n ) is said to be of type ( i, j ).

If m

If a new player feels that he or she needs assistance in learning the rules of craps, it is recommended to approach an empty craps table at a slow time of day ( for example, between 9 a. m. and 11 a. m .).

If k, m, and n are 1, so that and, then the Jacobian matrices of f and g are.

To make a figure larger or smaller is equivalent to multiplying the Cartesian coordinates of every point by the same positive number m. If ( x, y ) are the coordinates of a point on the original figure, the corresponding point on the scaled figure has coordinates

If the ambient temperature exceeds T < sub > m </ sub >, the homologous pairing of the sticky ends would not be stable because the high temperature disrupts hydrogen bonding.

If m and n are natural numbers and f ( x ) is a smooth ( meaning: sufficiently often differentiable ) function defined for all real numbers x in the interval, then the integral

This can be done for all m of the p < sub > i </ sub >, showing that m ≤ n. If there were any q < sub > j </ sub > left over we would have

* If m is a non-negative integer, then gcd ( m · a, m · b ) = m · gcd ( a, b ).

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 you drive greater distances than that, you'll just be skimming the surface and will never discover the enchantment, fascination and beauty which lured you in the first place to explore the hinterlands.

This belief is grounded in the Gospel of John passage “ You heard me say, ‘ I am going away and I am coming back to you .’ If you loved me, you would be glad that I am going to the Father, for the Father is greater than I.

If Acorn had thought to include this small modification in the original Electron design it is likely the machine would have had a much greater impact as it would have nearly doubled the amount of motion possible in games and saved modes 0 – 3 ( including the only 16 colour mode ) from being nearly useless due to contended memory timings.

If there is refraction at a collective spherical surface, or through a thin positive lens, O ' 2 will lie in front of O ' 1 so long as the angle u2 is greater than u1 ( under correction ); and conversely with a dispersive surface or lenses ( over correction ).

If debts are greater than $ 250, 000, the proposal must be filed under Division 1 of Part III of the Bankruptcy and Insolvency Act.

If you cannot change your own life, it must be that some greater force controls the world.

If there is a significant ( greater than 10 %) difference between cylinders, that may be an indication that valves or cylinder head gaskets are leaking, piston rings are worn or that the block is cracked.

He is still seeking greater autonomy from China, although Dolma Gyari, deputy speaker of the parliament-in-exile has stated " If the middle path fails in the short term, we will be forced to opt for complete independence or selfdetermination as per the UN charter ".

If, for the same focal length setting, the subject distance is adjusted to provide the same field of view at the subject, at the same f-number and final-image size, the smaller format has greater DOF, as with the “ same picture ” comparison above.

If the diet plan includes a daily caloric intake greater than the basal metabolic rate ( BMR ), the person will most likely lose fat.

If the width of the slits is greater than the wavelength, the Fraunhofer diffraction equation gives the intensity of the diffracted light as:

If the barbarians are successful in their attack ( if they have a strength greater than Catan ), then the players must pay the consequence.

:“ If an integer n is greater than 2, then has no solutions in non-zero integers a, b, and c. I have a truly marvelous proof of this proposition which this margin is too narrow to contain .”

If pain is chosen over pleasure in some cases it is only because it leads to a greater pleasure.

If ΔH is positive, the reaction is endothermic, that is heat is absorbed by the system due to the products of the reaction having a greater enthalpy than the reactants.

If we do not attempt to look back at an event, the greater the interval time between the time when the event from happening and the time when we try to remember, the memory will start to fade.

If a laser is swept across a distant object, the spot of laser light can easily be made to move across the object at a speed greater than c. Similarly, a shadow projected onto a distant object can be made to move across the object faster than c. In neither case does the light travel from the source to the object faster than c, nor does any information travel faster than light.

If the arguments are both greater than zero then the algorithm can be written in more elementary terms as follows:

If God exists in the understanding, we could imagine Him to be greater by existing in reality.

If the symbol width is n, the codes of width n + 1 fall naturally into two blocks: the lower block of 2 < sup > n </ sup > codes for coding single symbols, and the upper block of 2 < sup > n </ sup > codes that will be used by the decoder for sequences of length greater than one.

If the amount of orthopyroxene is substantially greater than the amount of clinopyroxene, the rock is then a norite.

If the event remains tied, the jumpers have a jump-off, beginning at the next greater height.

If these ratios are averaged using an arithmetic mean ( a common error ), high data points are given greater weights than low data points.

If the MRP is greater than a firm's Marginal Cost, then the firm will employ the worker since doing so will increase profit.