Help


[permalink] [id link]
+
Page "Monotonic function" ¶ 5
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

If and order
If the old fool argues about the price, tell him I shall order my husband not to treat him as a patient any longer.
If communications work, his decision would be instantly known in all command posts that would originate the actual go order.
If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.
If we grasp this opportunity to build an age of productive partnership between the less fortunate nations and those that have already achieved a high state of economic advancement, we will make brighter the outlook for a world order based upon security and freedom.
If obeyed, the law brings order and satisfaction.
If it is decided to make a small shift which may be required from military aid or special assistance funds, in order to carry out the purposes of the Mutual Security Act through this new peaceful program, this will be a hopeful sign to the world.
If not, how long to order and what is the price ''??
If possible, he should make an appointment in order that all persons involved may be present.
If elements in the sample space increase arithmetically, when placed in some order, then the median and arithmetic average are equal.
If we neglect higher than first order terms in the fluctuations, the mass balance equation becomes
If a planet is found to rotate slower than expected, then astronomers suspect that the planet is accompanied by a satellite, because the total angular momentum is shared between the planet and its satellite in order to be conserved.
If a player is one point away from winning a match, that player's opponent will always want to double as early as possible in order to catch up.
If a house or car is above a certain value, the bankrupt can buy the interest back from the estate in order to keep the asset.
If there is still a tie, each atom in each of the two lists is replaced with a sub-list of the other atoms bonded to it ( at distance 3 from the stereocenter ), the sub-lists are arranged in decreasing order of atomic number, and the entire structure is again compared atom by atom.
If a pixel-by-pixel ( image order ) approach to rendering is impractical or too slow for some task, then a primitive-by-primitive ( object order ) approach to rendering may prove useful.
If the hoop is the hoop in order for the striker ’ s ball, the striker earns a bonus stroke.
If two cofinal subsets of B have minimal cardinality ( i. e. their cardinality is the cofinality of B ), then they are order isomorphic to each other.
If, after that, they breach the order, proceedings can be started and in theory the person involved can be sent to prison.
If the case is dismissed, creditors will look to non-bankruptcy law in order to satisfy their claims.
If the first letters are the same, then the second letters are compared, and so on, until the order is decided.
If each pixel on the display actually contains three rectangular subpixels of red, green, and blue, in that fixed order, then things on the screen that are smaller than one full pixel in size can be rendered by lighting only one or two of the subpixels.
If we insert vertices in random order, it turns out ( by a somewhat intricate proof ) that each insertion will flip, on average, only O ( 1 ) triangles – although sometimes it will flip many more.
" If we cannot move on to point B until we have proved point A, and if in order to prove point A we must establish it with absolute certainty, then it looks as though we will have a very hard time proving any point at all.
If several planets in the same system are discovered at the same time, the closest one to the star gets the next letter, followed by the other planets in order of orbital size.

If and
* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) c a ( T ) for all such step regions S and T, then a ( Q )
If not, the curve is subdivided parametrically into two segments, 0 t 0. 5 and 0. 5 t 1, and the same procedure is applied recursively to each half.
# If the remainder from dividing N by 6 is not 2 or 3 then the list is simply all even numbers followed by all odd numbers N
This can be done for all m of the p < sub > i </ sub >, showing that m n. If there were any q < sub > j </ sub > left over we would have
If i 0, then exit the loop.
One can use that instruction, which is usually faster than a comparison against some arbitrary value ( requiring a subtraction ), to implement the command " If i 0, then exit the loop ".
# If A and B are Lebesgue measurable and A is a subset of B, then λ ( A ) λ ( B ).
* We are allowed to " add inequalities ": If a b and c d, then a + c b + d
* We are allowed to " multiply inequalities with positive elements ": If a b and 0 c, then ac bc.
If a preorder is also antisymmetric, that is, a b and b a implies a = b, then it is a partial order.
If the preorder is anti-symmetric, hence a partial order "≤", the equivalence is equality, so the relation "<" can also be defined as a < b if and only if ( a b and a ≠ b ).
If X is a real-valued random variable and a is a number then the event X a is the set of outcomes whose corresponding value of X is less than or equal to a.
: If a b and b a then a = b ( antisymmetry );
: If a b and b c then a c ( transitivity );

If and definition
If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.
If Bultmann's own definition of myth is strictly adhered to ( and it is interesting that this is almost never done by those who make such pronouncements ), the evidence is overwhelming that he does not at all exaggerate the extent to which the mythological concepts of traditional theology have become incredible and irrelevant.
If we define tangent covectors in terms of equivalence classes of smooth maps vanishing at a point then the definition of the pullback is even more straightforward.
If we consider the thesis and its converse as definition, then the hypothesis is an hypothesis about the application of the mathematical theory developed from the definition.
If one employs the strict, limited definition of crannog which requires the use of timber, then sites in the Western Isles are stricken from the discussion.
If the XML document type declaration includes any SYSTEM identifier for the external subset, it can't be safely processed as standalone: the URI should be retrieved, otherwise there may be unknown named character entities whose definition may be needed to correctly parse the effective XML syntax in the internal subset or in the document body ( the XML syntax parsing is normally performed after the substitution of all named entities, excluding the five entities that are predefined in XML and that are implicitly substituted after parsing the XML document into lexical tokens ).
If one concept is defined by another, and the other is defined by the first, this is known as circular definition, somewhat similar to a circular reasoning: neither offers us any enlightenment about what we wanted to know.
If ' beauty ' is defined as ' aesthetically successful ', one must continue to break down and define the following definition.
If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would ( by definition ) be outside the observable universe, it is difficult to imagine ( much less construct ) experiments to test this hypothesis.
If R is an integral domain then any two gcd's of a and b must be associate elements, since by definition either one must divide the other ; indeed if a gcd exists, any one of its associates is a gcd as well.
If the term has nonetheless retained a certain consistency in its use across these fields and would-be movements, it perhaps reflects the word ’ s position in general English usage: though the standard dictionary definition of irreal gives it the same meaning as unreal, irreal is very rarely used in comparison with unreal.
If the particles are indistinguishable, this is impossible by definition ; either particle can be in either state.
In 2001, David Wiley criticized learning object theory in his paper, The Reusability Paradox which is summarized by D ' Arcy Norman as, If a learning object is useful in a particular context, by definition it is not reusable in a different context.
Most states followed the federal definition of interrogation Innis rule If “ Yes ” go to 2 ; If “ No ”, Miranda does not apply.
If only the second and third conditions of the definition of measure above are met, and takes on at most one of the values, then is called a signed measure.
Proof: If there is no possible move, then the lemma is vacuously true ( and the first player loses the normal play game by definition ).
If a great number of attributes end up being the same as on the definition, a great amount of information can be " inherited ", and not have to be redundantly specified in the netlist, saving space, and making the design easier to read by both machines and people.
If the future was given the definition of Physics, it can be drawn down to this.
If ( x, y ) is a point on the parabola then, by Pappus ' definition of a parabola, it is the same distance from the directrix as the focus ; in other words:
The algorithm for deciding this is conceptually simple: it constructs ( the description of ) a new program t taking an argument n which ( 1 ) first executes program a on input i ( both a and i being hard-coded into the definition of t ), and ( 2 ) then returns the square of n. If a ( i ) runs forever, then t will never get to step ( 2 ), regardless of n. Then clearly, t is a function for computing squares if and only if step ( 1 ) terminates.
He also has a simple definition for talent in writing: " If you wrote something for which someone sent you a check, if you cashed the check and it didn't bounce, and if you then paid the light bill with the money, I consider you talented.
If the center is a distinguished point considered as origin of E, as in a normed space, it is not mentioned in the definition and notation.
If the average speed and time of travel is known, distance traveled can be found by a rearrangement of the definition, leaving us with:

0.468 seconds.