Therefore, if the sense of touch is functioning normally and there is a complete absence of spatial awareness in a psychically-blind person when the eyes are closed and an object is handled, the conclusion seems unavoidable that touch by itself cannot focus and take possession of the third-dimensionality of things and that actual sight or visual representations are necessary.

Therefore, any measures taken in peacetime which will decrease force requirements in war will contribute greatly to success when hostilities occur.

Therefore it was a major landmark when in 1865 Johann Josef Loschmidt measured the size of the molecules that make up air.

Therefore, when a runner on first or second base tags on a fly ball and advances no further than third base, no sacrifice is given and the batter is charged with an at-bat.

Therefore, when played by experts, Dots and Boxes becomes a battle for control: An expert player tries to force their opponent to start the first long chain.

Therefore, when continuum mechanics refers to a point or particle in a continuous body it does not describe a point in the interatomic space or an atomic particle, rather an idealized part of the body occupying that point.

Therefore, although the priest ( or minister ) says, " The body of Christ ", when administering the host, and, " The blood of Christ ", when presenting the chalice, the communicant who receives either one receives Christ, whole and entire.

Therefore, while Gibbon was pointing out what he perceived as a flaw in Eusebius's work, he also paid him a compliment, where by calling him ' grave ' he was ascribing the quality of sternness and a lack of credulity when it came to sifting out the fantastical from the reliable historical sources.

Therefore this formula only applies when is at least as large as.

Therefore, under certain conditions, when the orbitals of the unpaired outer valence electrons from adjacent atoms overlap, the distributions of their electric charge in space are further apart when the electrons have parallel spins than when they have opposite spins.

Therefore, it is equally likely to flip 21 heads as it is to flip 20 heads and then 1 tail when flipping a fair coin 21 times.

Therefore, he cannot avoid referring to “ the other side ” of the Doge ’ s figure when discussing his “ royal appearing show ”.

Therefore, in 1950 the World Fellowship of Buddhists inaugurated in Colombo unanimously decided that the term Hīnayana should be dropped when referring to Buddhism existing today in Sri Lanka, Thailand, Burma, Cambodia, Laos, etc.

Therefore, evidence of when human skin darkened has been used to date the loss of human body hair, assuming that the dark skin was needed after the fur was gone.

Therefore, IPv6 routers do not need to recompute a checksum when header fields ( such as the time to live ( TTL ) or hop count ) change.

Therefore, it is unclear when the ambitions railway expansion plan will be carried out.

Therefore, if the determinant equals zero then the parallelogram has no area, and that will happen when two vectors are on the same line.

Therefore, supporters of gun rights generally consider the use of the phrase " assault weapon " to be pejorative when used to describe these civilian firearms, and this term is seldom used outside of the United States in this context.

Therefore, looking at an image of oneself with the front / back axis flipped is the same as looking at an image with the left / right axis flipped and the whole figure rotated 180 degrees about the vertical axis, which is exactly what one sees when standing in front of a mirror.

Therefore we hold that every woman must possess the power and freedom to prevent conception except when these conditions can be satisfied.

Therefore, when a merger with a controlling stockholder was: 1 ) negotiated and approved by a special committee of independent directors ; and 2 ) conditioned on an affirmative vote of a majority of the minority stockholders, the business judgment standard of review should presumptively apply, and any plaintiff ought to have to plead particularized facts that, if true, support an inference that, despite the facially fair process, the merger was tainted because of fiduciary wrongdoing .″

Therefore, the pixel grid is divided into single-color regions that contribute to the displayed or sensed color when viewed at a distance.

For example, the prime number theorem states that the number of prime numbers less than or equal to N is asymptotically equal to N / ln N. Therefore the proportion of prime integers is roughly 1 / ln N, which tends to 0.

Therefore players get 1 to 2 for the numbers 4 and 10, 2 to 3 for the numbers 5 and 9, and 5 to 6 for the numbers 6 and 8.

Therefore, the energy eigenstates may be classified by two angular momentum quantum numbers, ℓ and m ( both are integers ).

Therefore, any eigenstate of the electron in the hydrogen atom is described fully by four quantum numbers.

Therefore P ( A to B ) actually consists of 16 complex numbers, or probability amplitude arrows.

Therefore, it is useful to check the carry flag after adding or subtracting numbers that are interpreted as unsigned values.

Therefore, it is useful to check the overflow flag after adding or subtracting numbers that are represented in two's complement form ( i. e. they are considered signed numbers ).

Therefore, another statement of Goldbach's conjecture is that all even integers greater than or equal to 4 are Goldbach numbers.

Therefore, a set of real numbers is bounded if it is contained in a finite interval.

Therefore the other p < sup > k </ sup > − p < sup > k − 1 </ sup > numbers are all relatively prime to p < sup > k </ sup >.

Therefore the space is recommended in the SI / ISO 31-0 standard, and the International Bureau of Weights and Measures states that " for numbers with many digits the digits may be divided into groups of three by a thin space, in order to facilitate reading.

Therefore, if we multiply together the numbers in each sequence, the results must be identical modulo p:

To start with, none of the terms a, 2a, ..., ( p − 1 ) a can be congruent to zero modulo p, since if k is one of the numbers 1, 2, ..., p − 1, then k is relatively prime with p, and so is a, so Euclid's lemma tells us that ka shares no factor with p. Therefore, at least we know that the numbers a, 2a, ..., ( p − 1 ) a, when reduced modulo p, must be found among the numbers 1, 2, 3, ..., p − 1.

Therefore, in linear algebra over the complex numbers, it is often assumed that a symmetric matrix refers to one which has real-valued entries.

Therefore in 1867 all existing lightships were given numbers by which they would be permanently identified, and the station at which they were presently serving was painted on their sides, to be changed as needed.

Therefore, according to the law of large numbers, the proportion of heads in a " large " number of coin flips " should be " roughly 1 / 2.

Therefore: can the correlation numbers such as

Therefore the product of zero numbers is 1.

Therefore, the person says, all odd numbers are prime.