Thus if a represents Socrates then Phil ( a ) asserts the first proposition, p ; if a instead represents Plato then Phil ( a ) asserts the second proposition, q.

Thus Legendre's contribution lay in introducing a convenient notation that recorded quadratic residuosity of a mod p. For the sake of comparison, Gauss used the notation, according to whether a is a residue or a non-residue modulo p.

Thus there is a number x ≡ ( q − 1 )< sup >( p − 2 )</ sup > for which ( q − 1 )· x ≡ 1 ( mod p ), and therefore a number k for which ( q − 1 )· x − 1 = kp.

Thus the initial assumption that p and q − 1 are relatively prime is untenable.

Thus represents a sequence of three phonemes,, ( the word push in standard English ), while represents the phonetic sequence of sounds ( aspirated " p "),, ( the usual pronunciation of push ).

Thus, the block and tackle reduces the input force by the factor p.

Thus, according to the law of non-contradiction, p must be false.

Thus, according to the law of non-contradiction, " not p " must be false, and so, according to the law of the excluded middle, p is true.

Thus p and C

Thus ( Irenaeus, i. 30, p. 109 ) the first archon sent Moses, Joshua, Amos, and Habakkuk ; the second Samuel, Nathan, Jonah, and Micah ; the third Elijah, Joel, and Zechariah ; the fourth Isaiah, Ezekiel, Jeremiah, and Daniel ; the fifth Book of Tobit and Haggai ; the sixth Micah ( qu.

Thus he says, " Not only is matter eternal, but form is potentially inherent in matter ; otherwise, it were a creation ex nihilo " ( Munk, " Mélanges ," p. 444 ).

Thus he says, " Not only is matter eternal, but form is potentially inherent in matter ; otherwise, it were a creation ex nihilo " ( Munk, " Mélanges ", p. 444 ).

Q containing these elements contains all the roots of p. Thus

Thus its activity a = p / p * will go to unity.

Thus denoting the common side as a and the diagonals as p and q, in every rhombus

Thus, according to Euler's quadrilateral theorem, the circumradius can be expressed in terms of the diagonals p and q, and the distance x between the midpoints of the diagonals as

Thus if U < sub > p </ sub >, V < sub > p </ sub >, Y < sub > p </ sub > are three tangent vectors at p and a and b are real numbers, then

Thus, means " belief / faith in the Æsir / gods ".

Thus, ATP was a simple request / response exchange, with no need to set up or tear down connections.

Thus, study of this Barnum / Forer effect has been mostly focused on the level of acceptance of fake horoscopes and fake astrological personality profiles.

Thus if the instrument depends on the pressure or suction effect alone, and this pressure or suction is measured against the air pressure in an ordinary room, in which the doors and windows are carefully closed and a newspaper is then burnt up the chimney, an effect may be produced equal to a wind of 10 mi / h ( 16 km / h ); and the opening of a window in rough weather, or the opening of a door, may entirely alter the registration.

Thus for an ion which traverses a 1 m flight path, across a time of 2000 ns, given an initial accelerating voltage of 5000 V and noting that one amu is 1 × 10 < sup >− 27 </ sup > kg, the mass-to-charge ratio ( more correctly the mass-to-ionisation value ratio ) becomes Z amu / charge.

Thus, the broadcast domain is the entire inter-connected layer two network, and the segments connected to each switch / bridge port are each a collision domain.

Thus, a robust surveillance system involving human clinicians and veterinarians may identify a bioweapons attack early in the course of an epidemic, permitting the prophylaxis of disease in the vast majority of people ( and / or animals ) exposed but not yet ill.

Thus in the presence of large quantum computers an n-bit key can provide at least n / 2 bits of security.

Thus a circular geosynchronous orbit has a radius of 42164 km ; 42164 / 6378. 1

Thus, Daodejing can be translated as " The Classic / Canon of the Way / Path and the Power / Virtue ," etc.

Thus a representation that compresses a 10MB file to 2MB has a compression ratio of 2 / 10

Thus a representation that compresses a 10MB file to 2MB would yield a space savings of 1-2 / 10 =

Thus, with a bus frequency of 100 MHz, DDR SDRAM gives a maximum transfer rate of 1600 MB / s.

Thus in Modern Greek, Eta is pronounced and represents the sound / i / ( a close front unrounded vowel ).

Thus it is 1 volt ( 1 joule per coulomb, 1 J / C ) multiplied by the electron charge ( 1 e, or ).

In the field of high-energy particle physics, the fundamental velocity unit is the speed of light c. Thus, dividing energy in eV by the speed of light in vacuum, one can describe the momentum of an electron in units of eV / c.

Thus Zheng became Qin Shi Huang, abolishing the system where the huang / di titles were reserved to dead and / or mythological rulers.

Thus, 1 g / dL

Thus 360 / 30s with this added cost feature could run 1401 programs and the larger 360 / 65s could run 7094 programs.

Thus 2 < sup >( q − 1 ) x </ sup >/ 2 < sup > kp </ sup >

Thus, F (− q ) has the same magnitude as F ( q ) but they have the opposite phase, i. e., φ ( q ) = − φ ( q )

Thus for English the " e " box is the largest while the " j ", " k ", " q ", " x ", and " z " boxes are the smallest.

Thus the efficiency depends only on q < sub > C </ sub >/ q < sub > H </ sub >.

Thus, if one of the coordinates, say q < sub > k </ sub >, does not appear in the Lagrangian, the right-hand side of the equation is zero, and the left-hand side requires that

Thus, the absence of the ignorable coordinate q < sub > k </ sub > from the Lagrangian implies that the Lagrangian is unaffected by changes or transformations of q < sub > k </ sub >; the Lagrangian is invariant, and is said to exhibit a symmetry under such transformations.

Thus one can define a ( unique ) unitary group of dimension n for the extension F < sub > q² </ sub >/ F < sub > q </ sub >, denoted either as U ( n, q ) or U ( n, q² ) depending on the author.

Thus, b < sub > q </ sub > is a symmetric bilinear form over K with matrix A. Conversely, any symmetric bilinear form b defines a quadratic form

Thus, this picture can be taken as a picture of eta as a function of q.

Thus the compound p → q is false if and only if both p is true and q is false.