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If and X
* If numbers have mean X, then.
* 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 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.
If we try to choose an element from each set, then, because X is infinite, our choice procedure will never come to an end, and consequently, we will never be able to produce a choice function for all of X.
If the automorphisms of an object X form a set ( instead of a proper class ), then they form a group under composition of morphisms.
If a detector was placed at a distance of 1 m, the ion flight times would be X and Y ns.
If X and Y are Banach spaces over the same ground field K, the set of all continuous K-linear maps T: X → Y is denoted by B ( X, Y ).
If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.
* Theorem If X is a normed space, then Xis a Banach space.
If Xis separable, then X is separable.
If F is also surjective, then the Banach space X is called reflexive.
* Corollary If X is a Banach space, then X is reflexive if and only if Xis reflexive, which is the case if and only if its unit ball is compact in the weak topology.
If there is a bounded linear operator from X onto Y, then Y is reflexive.
The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

If and .
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.

If and certificate
If requested the birth or adoption can be re-registered, thereby allowing the certificate to be issued without reference to the name registered at birth.
If there is suspicion of SSL being intercepted, one can examine the certificate associated with any secure web site, the root certificate should indicate whether it was issued for the purpose of intercepting.
Per John Jr., " If you look on his death certificate he choked on his own vomit and blood.
If an individual dies outside of his / her state of residence, the coroner of the state in which the death took place issues the death certificate.
If the student completed only six years, a certificate was given.
If there are no oppositions, or any oppositions are overcome, a certificate of registration will issue.
If student has got an additional certificate from foreign language ( IELTS, TOEFL, CAE, FCE ), at least at level B1, he
If an extension is critical and the system processing the certificate does not recognize the extension or cannot process it, the system MUST reject the entire certificate.
If, in this example, the private key was found and nobody had access to it, the status could be reinstated, and the certificate is valid again, thus removing the certificate from future CRLs.
If a certificate is mistakenly revoked, significant problems can arise.
If acceptance of a certificate fails in the absence of an available valid CRL, then no operations depending upon certificate acceptance can take place.
If the user trusts the CA and can verify the CA's signature, then he can also assume that a certain public key does indeed belong to whoever is identified in the certificate.
If accepted into one of the college's four certificate programs, students of any major complete a self-designed series of courses that relate to their academic interest, complete a college-funded summer internship, and complete an integrative project in their senior year.
If the shotgun is classified as a firearm ( where capacity exceeds 3 cartridges ) the firearm certificate ( FAC ) will need to show permission for the purchase of a suppressor.
If the apprentices are successful they are awarded with the journeymans's certificate ( Gesellenbrief ) and are now allowed to call themselves journeyman ( Geselle ).
If a sender wishes to enable email recipients to verify the sender's identity in the sense that a received certificate name carries the sender's name or an organization's name, the sender needs to obtain a certificate (" class 2 ") from a CA who carries out a more in-depth identity verification process, and this involves making enquiries about the would-be certificate holder.
* Certificate of No Impediment: If you are planning on marrying overseas ( not in the UK ), you may be required to provide the local authorities with a certificate of no impediment ( CNI ) as evidence that you are single and free to marry.

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