Without this capacity, which is often the case in practice, to produce a representation with lower resolution or lower fidelity than a given one, one needs to start with the original source signal and encode, or start with a compressed representation and then decompress and re-encode it ( transcoding ), though the latter tends to cause digital generation loss.

Without dubbing capability, an audio or video edit could not be done in-place on master cassette, and requires the editing output be captured to another tape, incurring generational loss.

Without loss of generality we assume

Without hormone replacement therapy ( HRT ), typical symptoms ( similar to those experienced by menopausal women ) include hot flashes, gradual bone-density loss resulting in osteopenia or osteoporosis, and potential weight gain or redistribution of body fat to the hips / chest.

Without loss of generality, we will define the optical axis so that it coincides with the z-axis of a fixed coordinate system.

Without loss of generality we can assume at least 3 of these edges, connecting to vertices r, s and t, are blue.

Without loss of generality, we will take λ to be non-negative.

# REDIRECT Without loss of generality

Without loss of generality ( abbreviated to WLOG ; less commonly stated as without any loss of generality or with no loss of generality ) is a frequently used expression in mathematics.

Without loss of generality, the coordinate system can be shifted, such that the reference point is set to be the origin.

Without this drug, Jem ' Hadar go into severe withdrawal, resulting in loss of cognitive and motor functions.

Without loss of generality, assume that the first columns of are linearly independent.

Without loss of generality, let's assume that.

* Without loss of generality, a common expression in mathematical proofs

* Without loss of generality –

Without loss of generality, we can take this action to be effective.

Without loss of generality, it can be assumed that D is connected.

Without these subsidies, global deep-sea fisheries would operate at a loss of $ 50 million a year.

Without it dispersion causes the loss of integrity of the original waveshape and is seen as smearing of what were originally sharp edges in the picture.

Without the ATU, SWR from a mismatched antenna could cause reflections of power back into the transmitter, which will cause heating in the transmitter and significant power loss.

Without loss of generality, let there exist a function such that

Without loss of generality, we may eliminate the normal rotational symmetry by choosing the Cartesian coordinates such that the z-axis is aligned with the angular momentum vector L and the momentum hodographs are aligned as they are in Figure 7, with the centers of the circles on the y-axis.

This bonus is multiplied according to the contract ; if the contract is Guard Without, the gain or loss for a single hand score is adjusted by 40 points one way or the other.

* Without affecting the generality of the main objects, the Society shall have the following ancillary objects:

Without loss of generality, we can demand also that j ( M ) contains all its sequences of length λ.

Without loss of generality, we can consider only centered profiles which peak at zero.

Without loss of generality, consider firm 1's problem:

Without loss of generality, we can take the projection line to be the x-axis.

Without loss of generality, we can take that plane to be the yz-plane so that

Without loss of generality, choose a coordinate system so that the axis of revolution is the z axis.

Without loss of generality, this edge is usually chosen to be the closest one on a face, so that in parallel view this edge corresponds to the same one in a perspective view.

Without saying or seeming to say that in portraying the Sartoris and the Compson families Faulkner's chief concern is social criticism, we can say nevertheless that through those families he dramatizes his comment on the planter dynasties as they have existed since the decades before the Civil War.

Without careful qualification this can be misleading.

Without a system of values there can be no society.

Without that knowledge, without that capacity to think, you can easily become a victim of people who seek to take advantage of you ".

Without diagnosis and treatment, the infection can be fatal in one to six days ; mortality in untreated cases is approximately 100 %.

Without clear documentation, software can be hard to use — especially if it is very specialized and relatively complex like Photoshop or AutoCAD.

According to Tibor R. Machan, " Without a market in which allocations can be made in obedience to the law of supply and demand, it is difficult or impossible to funnel resources with respect to actual human preferences and goals.

Without data decoding, the carrier can be detected by much simpler ground antennas and receivers.

Without this restriction, bizarre maps ( using regions of finite area but infinite perimeter ) can require more than four colors.

Without any such logical operators of valence 0, these two constants can only be expressed using quantifiers.

Without first finding the radian frequency, the natural frequency can be found directly using:

Without intension of some sort, words can have no meaning.

Without proper strength and flexibility, throwers can become extremely injury prone, especially in the shoulder and elbow.

Without knowledge of the Bible there can be no peace in the life of the Church or of society, and outside of it there is no real and abiding good ; it is the one authority for the faith.

Without L cuts, a conversation between two people can feel like a tennis match.

Without efforts to damp this noise, it can approach 130 decibels ( dB ) with strong fields ( see also the subsection on acoustic noise ).

Without re-enacting scenes, artists can then manipulate the demo files to add cameras, tweak timing and lighting, and change the surroundings.

* Without an MDI frame window, floating toolbars from one application can clutter the workspace of other applications, potentially confusing users with the jumble of interfaces.

Terminator X's innovative scratching tricks can be heard on the songs " Rebel Without a Pause ,", " Night of the living Baseheads " and " Shut Em Down ".

Near the end of her time as governor general, Adrienne Clarkson stated: " My constitutional role has lain in what are called ' reserve powers ': making sure that there is a prime minister and a government in place, and exercising the right ' to encourage, to advise, and to warn '[...] Without really revealing any secrets, I can tell you that I have done all three.

Without altering the system, we can take multiple samples, which will have a range of values of k, but the system will always be characterized by the same λ.

In 2007 the media rights body Reporters Without Borders praised reforms to the criminal code ; journalists can no longer be jailed on defamation charges.

Without referential transparency, such difference can be easily made and utilized in programs.

Without taking symmetries into account, the number of possible games can be determined by hand with an exact formula that leads to 255, 168 possible games ( see Henry Bottomley, 2001, or Steve Schaeffer, 2002 ).

Without an article, the term can refer to the entirety of humanity ( also: " society in general ", " society at large ", etc.