Indeed, the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies at least one Planck volume.

Indeed, even alphabets constructed " from scratch ", i. e. not derived from Semitic, usually have similar forms to represent this sound, e. g. ; the creators of the Afaka and Ol Chiki scripts, each invented in different parts of the world in the last century, both attributed their vowels for ' O ' to the shape of the mouth when making this sound.

Indeed, many of the concepts are shared, although in each field the emphasis is different.

Indeed, before 1272 a hereditary and not necessarily royal Earldom of Chester had already been created several times, eventually merging in the crown each time.

) Indeed, if a space is Hausdorff then it is T < sub > 0 </ sub >, and each T < sub > 0 </ sub > regular space is Hausdorff: given two distinct points, at least one of them misses the closure of the other one, so ( by regularity ) there exist disjoint neighborhoods separating one point from ( the closure of ) the other.

Indeed, today, in Asia the urban agglomerations of Dhaka, Karachi, Mumbai, Delhi, Manila, Seoul and Beijing are each already home to over 20 million people, while the Pearl River Delta, Shanghai-Suzhou, Jakarta-Bandung and Tokyo are forecast to approach or exceed 40 million people each within the coming decade.

Observe first the following: if a is a limit point of S, then any finite collection C of open sets, such that each open set U ∈ C is disjoint from some neighborhood V < sub > U </ sub > of a, fails to be a cover of S. Indeed, the intersection of the finite family of sets V < sub > U </ sub > is a neighborhood W of a in R < sup > n </ sup >.

Indeed, there were distinct Irish and British church traditions, each with their own practices, and there was significant local variation even within the individual Irish and British spheres.

Indeed, the equation means that the acceleration of the curve has no components in the direction of the surface ( and therefore it is perpendicular to the tangent plane of the surface at each point of the curve ).

Indeed, by regulating the number of molecules passed in each direction, the demon could achieve a pressure difference instead of a temperature difference, or any combination of temperature and pressure differences ( possibly including lower pressure on the higher temperature side, depending on the variance in the speeds of the molecules ).

Indeed, several proverbs contradict each other — however they agree in as much as they are advising the player to pay attention to the stated situation.

Indeed, the organizational structure was rather complex, requiring the frequent involvement of the Joint Chiefs of Staff and the Army and Navy commanders each reporting to both the Secretary of War and the Secretary of the Navy.

Indeed, even when frankly describing the nightmare world which is his ultimate aim (" A world where the thought of each man will not be his own, but an attempt to guess the thought of his neighbor (...) Men will not work for money, but for prestige, the approval of their fellows – not judgment, but public polls ") Toohey makes no mention of any overt dictatorship or coercive apparatus.

Indeed, according to the Kochen-Specker theorem, in the quantum mechanical formalism it is impossible that, for a given quantum state, each one of these measurable properties ( observables ) has a determinate ( sharp ) value.

Indeed, the average intercarrier compensation rate ranges from 0. 1 cents per minute for traffic bound to an information service provider (“ ISP ”) to 5. 1 cents per minute for intrastate traffic bound to a subscriber of a small ( rural ) incumbent local exchange carrier ; individual rates can be as low as zero and as high as 35. 9 cents per minute — even though in each case basically the same transport and switching functions are provided.

Indeed relationships within the Emberizidae as defined here are uncertain with the possibility that each of the three main groups may not be all that closely related.

Indeed, Seekers shunned creeds ( see Free Christianity ) and each assembly tended to embrace a broad spectrum of ideas.

Indeed, inevitably so, given that finance and cryptography are each built upon multiple disciplines.

Indeed, the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies at least one Planck volume.

Indeed, Durham himself claims to have been through such a process several times, each time finding himself back in " the real world " after deletion, with there existing some plausible explanation as to why he believed himself to have been a Copy who was deleted, though with each successive experience of Copying himself and being deleted, he gradually became increasingly confident that the experiences were actually the result of his consciousness finding a logical interpretation in which it had not actually ceased, rather than each successive experience being ultimately true and real.

Indeed, if G acts on a vector space V over F, each simultaneous eigenspace for every element of G, if such exists, determines a multiplicative character on G ; the eigenvalue on this common eigenspace of each element of the group.

Indeed, with a much lower incidence of fog than any other airport in the United Kingdom due to a geological anomaly, Glasgow Prestwick has the reputation of being " Britain's only fog-free airport ".

Indeed, the reverse impact of urban structure upon human behaviour and upon thought is evidenced by both observational study and historical record.

Indeed, the new Japanese army used the same rank structure as the French.

Indeed, androgens are capable of altering the structure of the brain in several species, including mice, rats, and primates, producing sex differences.

Indeed, such waves are quenched as their structure is destroyed.

Indeed, modern mathematics has been defined in a very general sense as the study of abstract structures ( by the Bourbaki group: see discussion there, at algebraic structure and also structure ).

Indeed, pholcid spiders do have a short fang structure ( called uncate ).

Indeed, the siting of the Saxon Guildhall here was probably due to the amphitheatre's remains Excavations by MOLAS in 2000 at the entrance to Guildhall Yard exposed remains of the great 13th-century gatehouse built directly over the southern entrance to the Roman amphitheatre, which raises the possibility that enough of the Roman structure survived to influence the siting not only of the gatehouse and Guildhall itself but also of the church of St Lawrence Jewry whose strange alignment may shadow the elliptical form of the amphitheatre beneath.

Indeed, from the perspective of first-order logic, all cases of the fallacy of the undistributed middle are, in fact, examples of affirming the consequent or denying the antecedent, depending on the structure of the fallacious argument.

Indeed, several classic results in random graph theory show that even networks with no real topological structure exhibit the small-world phenomenon, which mathematically is expressed as the diameter of the network growing with the logarithm of the number of nodes ( rather than proportional to the number of nodes, as in the case for a lattice ).

Indeed, The African Witch ( 1936 ) is so rich in incident, character, and thematic possibility that it over-burdens its structure.

Indeed, an alteration of this structure could contribute to several symptoms observed in MECP2-deficient mice.

) Indeed, the Lambert, a UNESCO-listed site, was divided into apartments by the Rothschilds, and parts of the wooden structure are rotting ; the staircases are sagging, and the paint is cracked and discolored.

Indeed it is an unfinished project, and so information about its intended structure is limited.

" Indeed, it then became obvious to the Atommobile riders that the ice crystals were not solid, but a lattice-like structure that they pass through.

Indeed, Rosch and Lakoff, themselves chief advocates of prototype theory, have emphasized in their later works that the findings of prototype theory do not necessarily tell us anything about category structure.

Indeed, according to Kuroda many features of Shinto, for example the worshiping of mirrors and swords or the very structure of Ise Shrine ( Shinto's holiest and most important site ) are typical of Taoism.

Indeed, the structure of GP900 is similar to that of a family of glycoproteins known as mucins.

Indeed, a proof by E. Mark Gold showed that any formal language that has hierarchical structure capable of infinite recursion is unlearnable from positive evidence alone, in the sense that it is impossible to formulate a procedure that will discover with certainty the correct grammar given any arbitrary sequence of positive data in which each utterance occurs at least once.

Indeed, for the tourist visitor the aerial tramway gives the best available views of Borgo Maggiore, as the cars sweep low over the rooftops of the main town square.

Indeed, changing basis to fA gives

Indeed, some forms of self stabilization are incorporated into most modern computer and telecommunications networks, since it gives them the ability to cope with faults that were not foreseen in the design of the algorithm.

Indeed, the reason Creasy gives for the significance of many of the fifteen battles, is the very fact that they denied Middle Eastern / Far Eastern people groups access to European soil.

Indeed dancing, rather than Mai, gives Sugiyama the meaning in life that he was looking for.

Indeed, when a delirious Dawn is strapped to the electric chair, she gives a speech as if she were winning an Oscar:

Indeed, a 2004 report of the International Theological Commission, the body of theologians that officially gives theological advice to the pope, highlighted ways in which continuing research and growing consensus within the scientific community on the question of polygenism encourages Catholic theologians to consider ways of accommodating polygenism into their theological reflections.

Indeed, Bruce gives Jean-Paul strict orders never to engage Bane in combat — and when Jean-Paul does face Bane, only his modified gloves save Jean-Paul from being thrown to his death.