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If and viewed
If substance is the highest category and there is no substance, being, then the unity perceived in all beings by virtue of their existing must be viewed in another way.
If the large-scale Universe appears isotropic as viewed from Earth, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred ( or special ) observer or vantage point.
If a and b are coprime and a divides the product bc, then a divides c. This can be viewed as a generalization of Euclid's lemma.
If r represents an arbitrary element of R, f can be viewed as a right R-homomorphism so that, or f can also be viewed as a left R module homomorphism, where.
If the example with the colored bricks above is viewed as an unbounded knapsack problem, then the solution is to take three yellow boxes and three grey boxes.
Thus the set of all polynomials with coefficients in the ring R forms itself a ring, the ring of polynomials over R, which is denoted by R. The map from R to R sending r to rX < sup > 0 </ sup > is an injective homomorphism of rings, by which R is viewed as a subring of R. If R is commutative, then R is an algebra over R.
If Mary says she has no pair, but in fact she has a flush, her cards speak and her hand is viewed for its genuine value, that of a flush.
If viewed from a distance of 1 astronomical unit, it would span an angular diameter of 35 ° and shine at magnitude − 38.
If the file is stored on a server for on-demand streaming and this stream is viewed by 1, 000 people at the same time using a Unicast protocol, the requirement is:
If the Americas are viewed as a single continent ( named America ), then it is composed of the subcontinents of North America and South America, the land bridge of Central America, and the islands of the Antillas.
If, on the way to the shrine, these children cried their tears were viewed as signs of imminent and abundant rains.
* If is a topological space ( viewed as a category as above ) and is some small category, we can form the category of all contravariant functors from to, using natural transformations as morphisms.
( If inversion on the unit group is continuous in the subspace topology of R then the topology on the unit group viewed in R or in R × R as above are the same.
If he hoped for such a marriage as a route to power, he was unsuccessful, though his secret marriage to Katherine Parr, Elizabeth's guardian, in late April 1547 was viewed by some as an attempt to become close to the young princess.
If a multivariate dataset is visualised as a set of coordinates in a high-dimensional data space ( 1 axis per variable ), PCA can supply the user with a lower-dimensional picture, a " shadow " of this object when viewed from its ( in some sense ) most informative viewpoint.
If viewed in this light, historian Eric Van Young states that Iturbide's seizure of the crown " seems less cynical and idiosyncratic when it comes along at the end of the independence struggle.
When Smith viewed the edition, she asked her mother, " If people are so afraid of him, why doesn't someone write a letter asking whether he wants to have a war or not ?".
If the world is reflected in a mirror which switches the left and right side of the car, the " reflection " of this angular momentum " vector " ( viewed as an ordinary vector ) points to the right, but the actual angular momentum vector of the wheel still points to the left, corresponding to the extra minus sign in the reflection of a pseudovector.
If the magnitude of v < sub > 3 </ sub > were to describe a measurable physical quantity, that would mean that the laws of physics would not appear the same if the universe was viewed in a mirror.
If the final image is viewed at approximately
If the original image will be given greater enlargement, or viewed at
If an image is viewed on a low-resolution display medium such as a computer monitor,
If the image is to be viewed only on a low-resolution device, a larger CoC may be appropriate ;
If both input and output are real numbers, this ordered pair can be viewed as the Cartesian coordinates of a point on the graph of the function.

If and continuum
If a dancer is good, she suggests purely and superbly the fundamental mechanics of ancestry and progeny -- the continuum of mankind.
If is the momentum of all the particles in a volume, and the particles are treated as a continuum, then Newton's second law gives
If all organisms are on one physical continuum, then we should also be on the same moral continuum.
* If the continuum hypothesis holds then is the unique Parovicenko space, up to isomorphism.
If there is an additional term in the H matrix which is an extra phase rotation which varies from point to point, the continuum limit is the Schrödinger equation with a potential energy:
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 Zermelo – Fraenkel set theory ( ZFC ) is consistent, then neither the continuum hypothesis nor its negation can be proven from ZFC.
* If Martin's axiom and the negation of the continuum hypothesis both hold, then there is a non-free Whitehead group.
If the generalized continuum hypothesis holds, then a cardinal is strongly inaccessible if and only if it is weakly inaccessible.
If an appropriately trained professional, knowing what the subject of the investigation knew at the time and following their agency guidelines ( such as a force continuum ), would have used the same level of force or higher, then the standard is met.
If it were possible to construct a universe like the Way without quantum entanglement, the Geometry Stacks would most likely not exist, or if in existence, would not be tied to a quantum entanglement with a particular continuum.
If you combine ‘ The Daily Show ’ with ‘ The Tonight Show ’ with my gig on ‘ Sunday Morning ,’ I see them all as part of one continuum in a way.
* If κ is a limit and the continuum function is eventually constant below κ then < math > 2 ^
The Knudsen number is useful for determining whether statistical mechanics or the continuum mechanics formulation of fluid dynamics should be used: If the Knudsen number is near or greater than one, the mean free path of a molecule is comparable to a length scale of the problem, and the continuum assumption of fluid mechanics is no longer a good approximation.
If the " savages " like those he met while on his Beagle voyage were not of the same species as civilized Englishmen, he would not be able to draw the complete continuum he felt necessary.
If is time-independent, the system goes only into those states in the continuum that have the same energy as the initial state.
If the continuum hypothesis holds, all real closed fields with cardinality the continuum and having the η < sub > 1 </ sub > property are order isomorphic.
If these are the two extreme positions on a continuum of asymmetric thoracic and abdominal organ formation, situs ambiguus covers everything in between.
If the continuum is made up of gases ( as sound waves ), solids and liquids, including the Earth.
If the action space is a continuum between two numbers, the lower and upper delimiting numbers are placed at the bottom and top of the arc respectively, usually with a variable that is used to express the payoffs.
If humankind was just at one end of the continuum of animal life, it made sense to many people that criminals — who acted " beastly " and who lacked reasoned conscience — were biologically inferior beings.

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