Logically, there are just as many ways to get a criticism wrong as to get the criticism right.

Logically, it follows that a user should trust an HTTPS connection to a website if and only if all of the following are true:

Logically, MAC addresses are used in the Media Access Control protocol sub-layer of the OSI reference model.

Logically forums are organized into a finite set of generic topics ( usually with one main topic ) driven and updated by a group known as members, and governed by a group known as moderators.

Logically analytical propositions, for instance, are those in which all the non-logical parts can be replaced without change of truth value.

Logically, they are part of a single group, with a unified design theme and a sequence of values, even though ten years or more may have elapsed from the first to the last.

Logically if the test trials are so difficult that no items are recalled or if the correct answers to the non-recalled items are not given to the test subject, then minimal or no learning will occur.

Logically, since the Protodevilns are an altogether different enemy compared to the Zentradi, they must at least react differently than the Zentradis when exposed to music or only react to certain components of music ( i. e., Song Energy ).

The translator explains in a footnote in the Foreword, " Logically, of course, Huizinga is correct ; but as English prepositions are not governed by logic I have retained the more euphonious ablative in this sub-title.

Logically, trees are an important component of forest research, but the wide variety of other life forms and abiotic components in most forests means that other elements, such as wildlife or soil nutrients, are often the focal point.

Logically, the only way Marx has to express an identity of aggregated output prices and aggregated output values, is to say that both of the totals are equal to exactly the same quantity of abstract labour time.

Logically, an argument is held in discredit if the underlying premise is found, " So severely in error that there is cause to remove the argument from the proceedings because of its prejudicial context and application ...".

She goes on to say " Logically, if sex is natural and wholesome and semen is as healthy as sweat, there is no reason to interpret ejaculation as a hostile gesture.

" She goes on to say " Logically, if sex is natural and wholesome and semen is as healthy as sweat, there is no reason to interpret ejaculation as a hostile gesture.

Logically, it has a similar meaning to the if and only if coupler ⇔.

Logically, then, the first principle of the plan must be that it is not rigidly oriented toward any geographical area.

Logically then, it is only by these localized views that one religion's adherents may see others as inferior.

Muhammad Iqbal also rejects the argument stating, “ Logically speaking, then, the movement from the finite to the infinite as embodied in the cosmological argument is quite illegitimate ; and the argument fails in total .” For Iqbal the concept of the first uncaused cause is absurd, he continues: " It is, however, obvious that a finite effect can give only a finite cause, or at most an infinite series of such causes.

Logically this ought to be faster than the preceding music, which was Adagio then Largamente molto ( broadening — that is, slowing — a lot ), but most conductors slow down.

Logically, it should be moved downtown.

Logically a younger layer cannot slip beneath a layer previously deposited.

Logically, the Liberals ' deputy leader, William McMahon, should have succeeded Holt.

Logically, the Prolog engine tries to find a resolution refutation of the negated query.

Logically, it was preceded by two previous human-dominated empires.

Logically, this does not assure that the moon itself ( or even the camera ) existed at the time the photograph is supposed to have been taken.

Logically it follows, at the same moment in which the line ahead became definitively the order for battle, there was established the distinction between the ships ' of the line ', alone destined for a place therein, and the lighter ships meant for other uses.

Logically enough, this inscribed circle was centered on the railway station.

* Logically, too, The Lone Ranger never wins against hopeless odds ; i. e., he is never seen escaping from a barrage of bullets merely by riding into the horizon.

Logically, scholars assume that the Zhui Shu yields methods of cubic equations.

Logically, a beta node at the head of a branch of beta nodes is a special case because it takes no input from any beta memory higher in the network.

Logically therefore it was in the occupation of the crown alone, that is to say in the royal demesne.

Logically, students felt that they could complete similar residencies in higher-paying specialties in the same amount of time.

Logically, the number of inputs should be at least as great as the number of outputs.

Logically, the truth value of some proposition cannot be used to infer that the same proposition is necessarily true.

Logically, this argument is sound, given the huge impoverished industrial working class-then often far too poor to consume the goods produced by an industrialised economy.

Logically such DNA would not be vestigial in the sense of being the vestige of a functional structure.

It is possible to prove many theorems using neither the axiom of choice nor its negation ; such statements will be true in any model of Zermelo – Fraenkel set theory ( ZF ), regardless of the truth or falsity of the axiom of choice in that particular model.

He shifted attention from the study of individual varieties to the relative point of view ( pairs of varieties related by a morphism ), allowing a broad generalization of many classical theorems.

Compactness in this more general situation plays an extremely important role in mathematical analysis, because many classical and important theorems of 19th century analysis, such as the extreme value theorem, are easily generalized to this situation.

In spaces that are compact in this latter sense, it is often possible to patch together information that holds locally — that is, in a neighborhood of each point — into corresponding statements that hold throughout the space, and many theorems are of this character.

In this fashion, one can prove many important theorems in the class of compact spaces, that do not hold in the context of non-compact ones.

The original versions of his papers contained " many technical errors of varying degree "; when the collection was first published, the errors were corrected and it was found that this could be done without major changes in the statements of the theorems, with one exception — a claimed proof of the Continuum hypothesis.

Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions ( theorems ) from these.

The characteristic of the field is also significant ; many theorems for finite groups depend on the characteristic of the field not dividing the order of the group.

This division of coding theory into compression and transmission is justified by the information transmission theorems, or source – channel separation theorems that justify the use of bits as the universal currency for information in many contexts.

If an isomorphism can be found from a relatively unknown part of mathematics into some well studied division of mathematics, where many theorems are already proved, and many methods are already available to find answers, then the function can be used to map whole problems out of unfamiliar territory over to " solid ground " where the problem is easier to understand and work with.

However, in the 1930s Gödel's incompleteness theorems convinced many mathematicians that mathematics cannot be reduced to logic alone, and Karl Popper concluded that " most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently.

Separability is especially important in numerical analysis and constructive mathematics, since many theorems that can be proved for nonseparable spaces have constructive proofs only for separable spaces.

Many theorems from classical geometry hold true for this spherical geometry as well, but many do not ( see parallel postulate ).

An excellent example is Fermat's Last Theorem, and there are many other examples of simple yet deep theorems in number theory and combinatorics, among other areas.

The well-known aphorism, " A mathematician is a device for turning coffee into theorems ", is probably due to Alfréd Rényi, although it is often attributed to Rényi's colleague Paul Erdős ( and Rényi may have been thinking of Erdős ), who was famous for the many theorems he produced, the number of his collaborations, and his coffee drinking.

In pure and applied mathematics, he produced many results, proved many theorems, and proposed several conjectures.

We can apply the flux and these theorems to many disciplines in which we see currents, forces, etc., applied through areas.

Before universal algebra came along, many theorems ( most notably the isomorphism theorems ) were proved separately in all of these fields, but with universal algebra, they can be proven once and for all for every kind of algebraic system.

Category theory applies to many situations where universal algebra does not, extending the reach of the theorems.