** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).

** If a team is penalized in the final minute of a half and the penalty causes the clock to stop, the opposing team now has the right to have 10 seconds run off the clock in addition to the yardage penalty.

** Mind Transferral: If Xavier were to die, he could transfer his mind and powers to a host body.

** " If It Works, It's Not AI: A Commercial Look at Artificial Intelligence startups "

** If O takes center ( best move for him ), X should take the corner opposite the original, and proceed as detailed above.

** If O plays a corner or side-middle first, X is guaranteed to win:

** If the tie is between two clubs, then the tie is broken using the head-to-head goal difference ( without away goals rule )

** If the tie is between more than two clubs, then the tie is broken, using the games the clubs have played against each other:

** If the Competition Committee removes a penalty, the points are also removed

** If an error occurs at any state of the FSM process, the BGP session is terminated immediately and returned to the Idle state.

** If an error occurs, BGP moves to the Active state.

** If the router was unable to establish a successful TCP session, then it ends up in the Active state.

** If it is unsuccessful again, the FSM is reset to the Idle state.

** If there is an error it is because one of the fields in the Open message doesn ’ t match between the peers, e. g. BGP version mismatch, MD5 password mismatch, the peering router expects a different My AS.

** If there is no error, a Keepalive message is sent, various timers are set and the state is changed to OpenConfirm.

** If a Keepalive message is received and no timer has expired before reception of the Keepalive, BGP transitions to the Established state.

** If a timer expires before a Keepalive message is received, or if an error condition occurs, the router transitions back to the Idle state.

** If there is any error in the Update message then a Notification message is sent to the peer, and BGP transitions back to the Idle state.

** If a timer expires before a Keepalive message is received, or if an error condition occurs, the router transitions back to the Idle state.

** If A < sup > p </ sup > B and B < sup > p </ sup > C then A < sup > p </ sup > C.

** If A is preferred to B and C is infinitesimally close to B then A is preferred to C.

** April 20 – Cicero, in Rome, writes to Varro " If our voices are no longer heard in the Senate and in the Forum, let us follow the example of the ancient sages and serve our country through our writings, concentrating on questions of ethics and constitutional law.

** If the maximum DNL error is less than 1 LSB, then the converter is guaranteed to be monotonic.

** Haliotis brazieri f. hargravesi ( Cox, 1869 ) – synonym: Haliotis ethologus, the Mimic abalone, Haliotis hargravesi, the Hargraves ’ s abalone

** Haliotis ovina f. patamakanthini Dekker, Regter, & Gras, 2001 – synonym: Haliotis patamakanthini

** Haliotis tuberculata f. lamellosa Lamarck, 1822

** Haliotis varia f. dohrniana Dunker, 1863 – synonym: Haliotis dohrniana Dunker, 1863

** Haliotis varia f. planata G. B.

** for all f in X ′ there exists x in X with ǁxǁ ≤ 1, so that f ( x ) = ǁfǁ.

** L, 45 ; 421: 6 ; 253: f. 44 ' N5

** In circuit analysis and signal processing to represent natural frequency, related to frequency f by ω = 2πf

** H. vulgare f. distichon ( two-rowed barley )

** H. vulgare f. hexastichon ( six-rowed barley )

** Section 4 ( f ) of the Department of Transportation Act

** Tancred, Count of Syracuse ( f. 1104 )

** This follows by noting f < sub > ω </ sub >( n ) > 2 ↑< sup > n-1 </ sup > n > 3 ↑< sup > n-2 </ sup > 3 + 2, and hence f < sub > ω </ sub >( g < sub > k </ sub > + 2 ) > g < sub > k + 1 </ sub > + 2.

** A few English names are written with two lowercase " f " s: ffrench, ffoulkes, etc.

** even and odd functions, a function is odd if f ( x ) = – f (– x ) for all x

** the restriction of f to the interior of the closed ball is a homeomorphism onto the cell C, and

** ff represents ( voiceless labiodental fricative ), like English f, since Welsh f is pronounced like an English v.

** Transparency ( projection ), as in " foil " (< u > f < u > ilm < u > o </ u > ver < u > i </ u > ncandescent < u > l </ u > ight ) or " viewfoil "

** Friul pie, pia ( pious, f .) " press "