Intuitively, causation seems to require not just a correlation, but a counterfactual dependence.

Intuitively, it seems clear that the answer should be more than a half, since there are more plain cookies in bowl # 1.

Intuitively at least, it seems that Newton's theory of motion entails a good many more truths than does, say, Aristotle's theory-despite the fact that both are known to have flaws.

Intuitively, the probability that any single number is divisible by a prime ( or any integer ), p is 1 / p.

) Intuitively, is a quine, a function that returns its own source code ( Gödel number ), except that rather than returning it directly, passes its Gödel number to and returns the result.

Intuitively, a Lipschitz continuous function is limited in how fast it can change: for every pair of points on the graph of this function, the absolute value of the slope of the line connecting them is no greater than a definite real number ; this bound is called the function's " Lipschitz constant " ( or " modulus of uniform continuity ").

Intuitively, expected absolute difference grows, but at a slower rate than the number of flips, as the number of flips grows.

Intuitively, dim ( ker T ) is the number of independent solutions x of the equation Tx

Intuitively speaking, part of the graph of a function is rotated around an axis, and is modelled by an infinite number of hollow pipes, all infinitely thin.

Intuitively, the first Betti number of a space counts the maximum number of cuts that can be made without dividing the space into two pieces.

Intuitively, the linking number represents the number of times that each curve winds around the other.

Intuitively, a meander can be viewed as a road crossing a river through a number of bridges.

Intuitively, if both coins are tossed the same number of times, the first coin should turn up fewer heads than the second one.

Intuitively, we can view the hyperprior vector α as pseudocounts, i. e. as representing the number of observations in each category that we have already seen.

Intuitively, the lower the number needed to harm, the worse the risk-factor.

Intuitively, the process can be pictured as follows: first shrink the real line to the open interval (- π, π ) on the x-axis ; then bend the ends of this interval upwards ( in positive y-direction ) and move them towards each other, until you get a circle with one point ( the topmost one ) missing.

Intuitively, the distinction says merely that there is no canonical choice of where the origin should go in the space, because it can be translated anywhere.

Intuitively, one can say that the air follows the curve of the foil, but this is not very rigorous or precise.

Intuitively then, the oracle machine can perform all of the usual operations of a Turing machine, and can also query the oracle for an answer to a specific question of the form " is x in A?

Intuitively, this means there are computational limits on what can be proven by computer programs.

Intuitively, multiplying by a scalar r stretches a vector out by a factor of r. Geometrically, this can be visualized ( at least in the case when r is an integer ) as placing r copies of the vector in a line where the endpoint of one vector is the initial point of the next vector.

Intuitively, the reasoning is that, as web crawlers have a limit to how many pages they can crawl in a given time frame, ( 1 ) they will allocate too many new crawls to rapidly changing pages at the expense of less frequently updating pages, and ( 2 ) the freshness of rapidly changing pages lasts for shorter period than that of less frequently changing pages.

Intuitively, one can understand this second formulation by noting that an elastic band stretched between two points will contract its length, and in so doing will minimize its energy.

Intuitively, this finds the filter that is as close as you can get to the desired response given that you can use only N coefficients.

Intuitively, one can view a unit as the smallest testable part of an application.

Intuitively, represents a small perturbation in the index of T. By noting that and that is always between 0 and 1, can be used to ignore the floor function in the index.

Intuitively, we can think of this as being all meromorphic functions whose poles at every point are no worse than the corresponding coefficient in D ; if the coefficient in D at z is negative, then we require that h has a zero of at least that multiplicity at z – if the coefficient in D is positive, h can have a pole of at most that order.

Intuitively, one can think of the radical of I as obtained by taking all the possible roots of elements of I. Rad ( I ) turns out to be an ideal itself, containing I.

Intuitively, this is allowed in the antecedent because we can always restrict the scope of our proof ( if all cars have wheels, then it's safe to say that all black cars have wheels ); and in the succedent because we can always allow for alternative conclusions ( if all cars have wheels, then it's safe to say that all cars have either wheels or wings ).

If, for example, we simply look at a curve in the real affine plane there might be singular P modulo the stalk, or alternatively as the sum of m ( m − 1 )/ 2, where m is the multiplicity, over all infinitely near singular points Q lying over the singular point P. Intuitively, a singular point with delta invariant δ concentrates δ ordinary double points at P. For an irreducible and reduced curve and a point P we can define δ algebraically as the length of where is the local ring at P and is its integral closure.

Intuitively, a continuous curve in 2 or 3 ( or higher ) dimensions can be thought of as the path of a continuously moving point.

Intuitively, a system simulates another system if it can match all of its moves.

Intuitively, the theorem states that to build a VMM it is sufficient that all instructions that could affect the correct functioning of the VMM ( sensitive instructions ) always trap and pass control to the VMM.

Intuitively one wants to choose h as small as the data allow, however there is always a trade-off between the bias of the estimator and its variance ; more on the choice of bandwidth later.

Intuitively, one would expect systems which collect more than one type of data to be more useful than systems which collect only one type of information ( such as single-purpose laboratory or 911 call-center based systems ), and be less prone to false alarms, and this appears to be the case.

Intuitively, it should be

Intuitively, if one pulled and stretched out the paths in the maze in the proper way, the result could be made to resemble a tree.

Intuitively, theories of value must be important to ethics.

Intuitively this would seem to be folly because it would cool the iron.

Intuitively, the additivity property says that the probability assigned to the union of two disjoint events by the measure should be the sum of the probabilities of the events, e. g. the value assigned to " 1 or 2 " in a throw of a die should be the sum of the values assigned to " 1 " and " 2 ".

Intuitively, the divergence ( denoted ∇•) of a vector field is a measure of flux diverging radially outwards from a point, so the negative is the amount piling up at a point, hence the rate of change of density in a region of space must be the amount of flux leaving or collecting in some region ( see main article for details ).

Schubert wrote, " Intuitively, iterated limiting identification might be regarded as higher-order inductive inference performed collectively by an ever-growing community of lower order inductive inference machines.

Intuitively we would expect it to be even more unlikely for all 5 marbles to be white.