Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

Thus, the three main categories of antisubmarine warfare operations are defense of shipping, defense of naval forces, and area defense.

Thus, while it remains possible that the Babylonians and/or the Pythagoreans may perhaps have had the magic square of three before the Chinese did, more definite evidence will have to turn up from the Middle East or the Classical World before China can lose her claim to the earliest known magic square by more than a thousand years.

Thus two indices are used for a two dimensional array, three for a three dimensional array, and n for an n dimensional array.

Thus, three eclipse calculations may be evidence for the suggestion that Romulus reigned from 746 BC to 709 BC, and Rome was founded during 745 BC.

Thus, negotiation generally features only in games for three or more people.

Thus, an outdoors utility knife suited for camping or hunting might use a broad three to five-inch fixed blade, while a utility knife designed for the construction industry might feature a replaceable utility or razor blade for cutting packaging, cutting shingles, marking cut lines, or scraping paint.

Thus, for example, the English form is is an apparent cognate of German ist, Latin est and Russian < nowiki > jest '</ nowiki >, even though the Germanic, Italic, and Slavic language groups split at least three thousand years ago.

Thus, for example, there are three main isotopes of carbon.

Thus the overall ratios of the three coinages remained roughly equivalent.

Thus the first two games were played at Wrigley Field and the next three at the home of their opponents, San Diego.

Thus an equivalence relation over X, a partition of X, and a projection whose domain is X, are three equivalent ways of specifying the same thing.

Thus every proposition has three components: the two terms, and the " copula " that connects or separates them.

Thus, all three models for paramagnetic Hb-O < sub > 2 </ sub > may contribute to some small degree ( by resonance ) to the actual electronic configuration of Hb-O < sub > 2 </ sub >.

Thus as a result of the three Carnatic Wars, the British East India Company gained exclusive control over the entire Carnatic region of India.

Thus it happened that, with Hermes as their guide, the three candidates bathed in the spring of Ida, then confronted Paris on Mount Ida in the climactic moment that is the crux of the tale.

Thus three major themes in 19th century mathematics were combined by Lie in creating his new theory: the idea of symmetry, as exemplified by Galois through the algebraic notion of a group ; geometric theory and the explicit solutions of differential equations of mechanics, worked out by Poisson and Jacobi ; and the new understanding of geometry that emerged in the works of Plücker, Möbius, Grassmann and others, and culminated in Riemann's revolutionary vision of the subject.

Thus, every MUMPS command or function name could be abbreviated from one to three letters in length, e. g. Quit ( exit program ) as Q, $ P

Thus the Arabic word ثلاثة ( three ) is transliterated ṯalāṯah.

Thus, for example, the term " glucose " may signify glucofuranose, glucopyranose, the open-chain form, or a mixture of the three.

Thus Antony, as Caesar's key adherent and one of the two men around whom power coalesced following his assassination, was one of the three men chiefly responsible for the fall of the Roman Republic.

Thus, a player who bids three and takes either two or four tricks will lose one point.

Thus a collection of two lines is a couplet ( or distich ), three lines a triplet ( or tercet ), four lines a quatrain, and so on.

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, to cite but one example, the Pax Britannica of the nineteenth century, whether with the British navy ruling the seas or with the City of London ruling world finance, was strictly national in motivation, however much other nations ( e.g., the United States ) may have incidentally benefited.

Thus every part and plane of the picture keeps changing place in relative depth with every other part and plane ; ;

Thus, if one accelerometer is properly aligned, the other is also.

Thus some provinces contained tribes which detested each other, and to them independence meant an opportunity for war.

Thus, according to the character Pausanias in Plato's Symposium, Aphrodite is two goddesses, one older while the other younger.

This latter construal is sometimes expressed by saying " there is no fact of the matter as to whether or not P ." Thus, we may speak of anti-realism with respect to other minds, the past, the future, universals, mathematical entities ( such as natural numbers ), moral categories, the material world, or even thought.

The intense vomiting and occasional diarrhea it induces can clear the body of worms and other tropical parasites, and harmala alkaloids themselves have been shown to be anthelmintic Thus, this action is twofold ; a direct action on the parasites by these harmala alkaloids ( particularly harmine in ayahuasca ) works to kill the parasites, and parasites are expelled through the increased intestinal motility that is caused by these alkaloids.

Thus, it determines substancehood empirically by the togetherness of properties rather than by a bare particular or by any other non-empirical underlying strata.

Thus, as with other proposed megafauna cryptids, climate and food supply issues would make such a creature's survival in reported habitats unlikely.

Thus an understanding of how these two levels relate to each other is needed.

Thus, one nucleus offers a more tightly bound position to an electron than does another nucleus, with the result that one atom may transfer an electron to the other.

Thus the word retains two senses today, one architectural and the other ecclesiastical.

In his fictional historical essay " The Hyborian Age ", Howard describes how the people of Atlantis — the land where his character King Kull originated — had to move east after a great cataclysm changed the face of the world and sank their island, settling where Ireland and Scotland would eventually be located, Thus they are ( in Howard's work ) the ancestors of the Irish and Scottish ( the Celtic Gaels ) and not the Picts, the other ancestor of modern Scots who also appear in Howard's work.

Thus the concept ' computable ' is in a certain definite sense ' absolute ', while practically all other familiar metamathematical concepts ( e. g. provable, definable, etc.

Thus, humans must be other biological machines created by a life form just as the BETA are.

Thus references to a patriarchal Biblical culture may or may not be relevant to other societies.

Thus perceptions must already come parcelled into distinct " bundles " before they can be associated according to the relations of similarity and causality: in other words, the mind must already possess a unity that cannot be generated, or constituted, by these relations alone.

Thus the dragoon regiments of the Imperial German Army wore the pickelhaube ( spiked helmet ) of the same design as those of the infantry and the British dragoons wore scarlet tunics, In other respects however dragoons had adopted the same tactics, roles and equipment as other branches of the cavalry and the distinction had become simply one of traditional titles.

Thus, it is on the one side, the study of wealth and on the other and more important side, a part of the study of man.

Thus, a field due to any particular particle or time-varying electric or magnetic field contributes to the fields present in the same space due to other causes.

Thus, speakers of two adjacent Inuit dialects would usually be able to understand one another, but speakers from dialects distant from each other on the dialect continuum would have difficulty understanding one another.

Thus, when either field is changing in time, then a field of the other is necessarily induced.

Thus, churches actually had money-changing tables at which each coin would be examined separately and a token of actual worth given to the layperson so that he or she could be seen by the other parishioners as putting money in the basket during that part of the service.

Thus, the electromagnetic field may be viewed as a dynamic entity that causes other charges and currents to move, and which is also affected by them.