** 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 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.

** Well-ordering theorem: Every set can be well-ordered.

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

** Antichain principle: Every partially ordered set has a maximal antichain.

** For every non-empty set S there is a binary operation defined on S that makes it a group.

** Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion.

** In particular, the cofinality of any nonzero finite ordinal, or indeed any finite directed set, is 1, since such sets have a greatest element.

** In particular, let A be a set of size n, and consider the set of subsets of A containing no more than m elements.

** Mine Exploder T11: Six forward firing mortars to set off mines.

** " Has the same absolute value " on the set of real numbers

** " Has the same cosine " on the set of all angles.

** Filter ( mathematics ), a special subset of a partially ordered set

** The set of infinite strings is the inverse limit of the set of finite strings, and is thus endowed with the limit topology.

** Written communication ( writing ) – representation of language in a textual medium through the use of a set of signs or symbols ( known as a writing system ).

** Mouthpiece ( scuba ), a component of a scuba diving or industrial breathing set

** Metrics ( networking ), set of properties of a communication path

** Also an older term for the empty set

** 4 8 × 8 single-color user-defined sprites ; each sprite's color may be set independently