If you have taken this stroll in the morning, and you have the time and inclination, walk to the right along the crowded Corso for half a dozen blocks to visit the fine private collection of paintings -- mainly of the sixteenth and seventeenth centuries -- in the Palazzo Doria ( open Sunday, Tuesday, and Thursday, 10:00 to 1:00 ).

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

In 1997 Enya released her greatest hits collection, Paint the Sky with Stars: The Best of Enya, again a top five smash in the UK and Germany, which featured two new songs: " Paint the Sky with Stars " and " Only If ..."; " Only If ..." later became a single.

If a collection of atoms are in the excited state, spontaneous decay events to the ground state will occur at a rate proportional to N < sub > 2 </ sub >, the number of atoms in the excited state.

* If 26 Sets are drawn from a collection of 81 cards, the remaining 3 cards form a Set too.

Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.

Consider, for example cutlery: If one collection of cutlery is combined with another, we still have " cutlery.

* The Wheels of If and Other Science Fiction ( 1948 )-early collection of de Camp's short fiction, including " The Wheels of If "

In 2007, Welsh published If You Liked School You'll Love Work, his first collection of short stories in over a decade.

:‘ If to collect cigarette cards is a sign of eccentricity, how then will posterity judge one who amassed the biggest collection in the world?

If a collection B of subsets of X fails to satisfy either of these, then it is not a base for any topology on X.

If S is compact but not closed, then it has an accumulation point a not in S. Consider a collection consisting of an open neighborhood N ( x ) for each x ∈ S, chosen small enough to not intersect some neighborhood V < sub > x </ sub > of a.

If the function input x is an ordered pair ( x < sub > 1 </ sub >, x < sub > 2 </ sub >) of real numbers, the graph is the collection of all ordered triples ( x < sub > 1 </ sub >, x < sub > 2 </ sub >, f ( x < sub > 1 </ sub >, x < sub > 2 </ sub >)), and its graphical representation is a surface ( see three dimensional graph ).

He also released Acoustic Cafe, an album, that with the exception of " You Have My Heart ," is a collection of covers ranging from Bob Dylan (" If Not For You ," " Make You Feel My Love ") to Cyndi Lauper (" Time After Time ").

If a large collection of these devices were placed in a system, half of the devices had the ring at site A and half at B at any given moment in time.

If Königs statement was " correct ", according to which all " finitely definable " real numbers form a collection of cardinal number, this would imply the countability of the whole continuum ; but this is obviously wrong.

If such a collection of inner products on the tangent bundle of a manifold varies smoothly as one traverses the manifold, then concepts that were defined only pointwise at each tangent space can be extended to yield analogous notions over finite regions of the manifold.

If we define shamanism this way, Eliade claims, we find that the term covers a collection of phenomena that share a common and unique " structure " and " history ".

If every object in a collection of objects fails to have a certain property, then the probability that a random object chosen from the collection has that property is zero.

Reagon's work as a scholar and composer is reflected in publications on African American culture and history, including: a collection of essays entitled If You Don ’ t Go, Don ’ t Hinder Me: The African American Sacred Song Tradition ( University of Nebraska Press, 2001 ); We Who Believe In Freedom: Sweet Honey In The Rock: Still on the Journey, ( Anchor Books, 1993 ); and We'll Understand It Better By And By: Pioneering African American Gospel Composers ( Smithsonian Press, 1992 ).

Statements such as the Banach – Tarski paradox can be rephrased as conditional statements, for example, " If AC holds, the decomposition in the Banach – Tarski paradox exists.

If a player holds onto his stock, he runs the risk that the acquired chain may not reemerge before the game ends.

If the claim is unopposed, the Committee will generally award the claim, unless there is evidence of collusion, the peerage has been in abeyance for more than a century, or the petitioner holds less than one-third of the claim.

If a " clinch " – a defensive move in which a boxer wraps his or her opponents arms and holds on to create a pause – is broken by the referee, each fighter must take a full step back before punching again ( alternatively, the referee may direct the fighters to " punch out " of the clinch ).

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 the ruler lacks rén, Confucianism holds, it will be difficult if not impossible for his subjects to behave humanely.

If on the other hand Theorem 2 holds and φ is valid in all structures, then ¬ φ is not satisfiable in any structure and therefore refutable ; then ¬¬ φ is provable and then so is φ, thus Theorem 1 holds.

If all the non-zero bits were counted, then the intermediate result register now holds the final result.

If the judge finds such probable cause, he or she binds, or holds over, the suspect for trial.

If the condition only holds for all singleton subsets of R, then the ring is a right Rickart ring.

The Council of Trent decreed: " If anyone shall say that a man once justified can sin no more, nor lose grace, and that therefore he who falls and sins was never truly justified ; or, on the contrary, that throughout his whole life he can avoid all sins even venial sins, except by a special privilege of God, as the Church holds in regard to the Blessed Virgin: let him be anathema.

If denotes the state of the system at any one time t, the following Schrödinger equation holds:

If the foregoing argument holds good, Mary of Bethany and the " sinner " are one and the same.

If the most commonly accepted attribution of texts ( that of Christian Lindtner ) holds, then he was clearly a Māhayānist, but his philosophy holds assiduously to the Śrāvaka canon, and while he does make explicit references to Mahāyāna texts, he is always careful to stay within the parameters set out by the Śrāvaka canon.

If a player has two small pairs, and he believes that it will be necessary for him to make a full house to win, then he has four outs: the two remaining cards of each rank that he holds.

If P were 100 % true, not-P would be 100 % false, and there is no contradiction because P and not-P no longer holds.

If this condition is fulfilled, also holds.

If the opposite holds true, then it becomes more costly for landowners to have guards for the slaves than to employ paid workers who can only demand low wages due to the amount of competition.

If, we call X self-similar if it is the only non-empty subset of Y such that the equation above holds for.

If the axiom of choice holds, the following conditions on a cardinal are equivalent:

If the officer imposing punishment holds General Court Martial authority, or if the commanding officer of the grade O-7 or greater