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If the sets are short to medium length the caller will often try to run the dance until each couple has danced with every other couple both as a 1 and a 2 and returned to where they started.
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If and sets
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.
** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.
If the anchor continues to drag, or sets after having dragged too far, it should be retrieved and moved back to the desired position ( or another location chosen.
* The Lusternik – Schnirelmann theorem: If the sphere S < sup > n </ sup > is covered by n + 1 open sets, then one of these sets contains a pair ( x, − x ) of antipodal points.
If each player wins a set, or both sets end tied, there is a 3-end tiebreaker to determine a winner.
If two sets are used, each player controls two differently colored sets of pieces at opposite corners of the star.
If two sets are played, the pieces can either go into the opponent's starting corners, or one of the players ' two sets can go into an opposite empty corner.
If κ is an infinite cardinal number, then cf ( κ ) is the least cardinal such that there is an unbounded function from it to κ ; and cf ( κ ) = the cardinality of the smallest collection of sets of strictly smaller cardinals such that their sum is κ ; more precisely
If this precaution was not taken, the potential customers would be at the mercy of " 2 sets of carob seeds ".
Presheaves: If X is a topological space, then the open sets in X form a partially ordered set Open ( X ) under inclusion.
If the two sets of bodies do not have concurrent jurisdiction but, as in the case of the International Criminal Court ( ICC ), the relationship is expressly based on the principle of complementarity, i. e. the international court is subsidiary or complementary to national courts, the difficulty is avoided.
# If A is a disjoint union of countably many disjoint Lebesgue measurable sets, then A is itself Lebesgue measurable and λ ( A ) is equal to the sum ( or infinite series ) of the measures of the involved measurable sets.
A measure μ is monotonic: If E < sub > 1 </ sub > and E < sub > 2 </ sub > are measurable sets with E < sub > 1 </ sub > ⊆ E < sub > 2 </ sub > then
A measure μ is countably subadditive: If E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, … is a countable sequence of sets in Σ, not necessarily disjoint, then
A measure μ is continuous from below: If E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, … are measurable sets and E < sub > n </ sub > is a subset of E < sub > n + 1 </ sub > for all n, then the union of the sets E < sub > n </ sub > is measurable, and
If and are
If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;
If I even hint at it do you think it will matter that you are his nephew -- and not even a blood nephew ''??
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 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.
Defoe then commented, `` If they Could Draw that young Gentleman into Their Measures They would show themselves quickly, for they are not asham'd to Say They want only a head to Make a beginning ''.
If Jews are identified as a religious body in a controversy that comes before a national or international tribunal, it is obviously compatible with the goal of human dignity to protect freedom of worship.
Without preliminaries, Esther asked him, `` If you are a world citizen, will you take Garry Davis' place in his tent while he goes to the hospital ''??
If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.
If the would-be joiner asks these questions he is not likely to be duped by extremists who are seeking to capitalize on the confusions and the patriotic apprehensions of Americans in a troubled time.
If the record buyer's tastes are somewhat eclectic or even the slightest bit esoteric, he will find them satisfied on educational records.
If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.
If they are to be commended for foresight in their planning, what then is the judgment of a town council that compounds this problem during the planning stage??
If the Communists are sincere in wanting a united, neutral and disarmed Germany, it might well be advantageous for the German people in this nuclear age.
If only this could be done more often -- with such heartening results -- many of the earth's `` big problems '' would shrink to the insignificances they really are.
If any are left, presently, we may expect to see signs specifically prohibiting the feeding of them too.
If the raw population figures are crucially relevant, then it is idle to think of liberation, as idle as to suppose that Poland might liberate Russia.
If it is not enough that all of our internationalist One Worlders are advocating that we join this market, I refer you to an article in the New York Times' magazine section ( Nov. 12, 1961 ), by Mr. Eric Johnston, entitled `` We Must Join The Common Market ''.
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