* 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 the appellate court does find a legal defect in the decision " below " ( i. e., in the lower court ), it may " modify " the ruling to correct the defect, or it may nullify (" reverse " or " vacate ") the whole decision or any part of it.

If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

* 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 the resulting four kilobyte table size is too large for a given target platform, the table lookup operation can be performed with a single 256-entry 32-bit ( i. e. 1 kilobyte ) table by the use of circular rotates.

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 the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their perpendicular height of incidence, i. e. their distance from the axis.

If the ratio a '/ a be sufficiently constant, as is often the case, the above relation reduces to the condition of Airy, i. e. tan w '/ tan w = a constant.

If we define r < sub > i </ sub > as the displacement of particle i from the center of mass, and v < sub > i </ sub > as the velocity of particle i with respect to the center of mass, then we have

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 the auction is passed out, i. e. no bids are made and only four passes are called, the hands are abandoned and the turn to deal passes in rotation.

If a Banach algebra has unit 1, then 1 cannot be a commutator ; i. e., for any x, y ∈ A.

If your side has two aces and a void, then you are not at risk of losing the first two tricks, so long as ( a ) your void is useful ( i. e., does not duplicate the function of an ace that your side holds ) and ( b ) you are not vulnerable to the loss of the first two tricks in the fourth suit ( because, for instance, one of the partnership hands holds a singleton in that suit or the protected king, giving your side second round control ).

If one eigenvalue is negative ( i. e., an imaginary frequency ), then the stationary point is a transition structure.

If both high priority substituents are on the same side of the double bond, i. e. in the cis configuration, then the stereoisomer is assigned a Z or Zusammen configuration.

If a 4, 5, 6, 8, 9, or 10 is thrown on the come-out roll ( i. e., if a point is set ), most casinos allow pass line bettors to take odds by placing from one to five times ( and at some casinos, up to 100 times ) the pass line bet behind the pass line.

If two cofinal subsets of B have minimal cardinality ( i. e. their cardinality is the cofinality of B ), then they are order isomorphic to each other.

* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then

If the glass is cooled quickly in the absence of a strong light source by putting ice on the glass or placing it in the freezer with the door almost closed, it turns backwards ( i. e. the silver sides trail ).

If he had married her, he'd have been asking for trouble.

He said: `` If it's all right with you, Mr. Morgan, I'll sleep out here on the couch.

If we let them go, they won't stay away, they'll find men to ride with them and they'll be back.

He added, `` If this doesn't work out, the three of you barricade yourself in the house and talk terms with them ''.

If you've got any ideas ''.

If she did, he could stand it better in the light.

If you ever try anything without my orders I'll kill you ''.

`` If you hadn't I'd have killed you ''.

If she sensed any unusual preoccupation on the part of her mother, she did not comment upon it.

If she, Pamela, were being held responsible for his crimes, then hers must be the final act of expiation.

If, as she walked, her steps fumbled from time to time, she chose to ignore that omen.

If the slope grew steeper and the groves more dim, she tried not to heed.

If, when this was all over, she found the words to tell him about it, she wondered if he would ever understand.

If you take the one, you'd better take both ''.

If the bluff failed and they ran into trouble, Brannon had told the others, they would withdraw -- and he would come after his son another time.

If you don't leave this country within 3 days, your life will be taken the same as Powell's was.

If someone were to drop a match in here, this place would go up like a haystack ''.

If we was both armed, you wouldn't talk so tough ''.

`` If you spot Carmer give a yell before you move in ''.

If he wondered whether the attackers would allow him to pull away unmolested, he had his answer a moment later.

If the other pilots were worried, they did not show it.

If it were the enemy, tactically his position was correct.

If they're Japs.

If any of us miss, they can pick up the pieces.

If the turn was too tight, a barrel roll would bring them out.