Thus, intuitionists are ready to accept a statement of the form " P or Q " as true only if we can prove P or if we can prove Q:

Thus if we reason from the statement " Pegasus flies " to the statement " Pegasus exists ", we are not asserting that Pegasus is made up of atoms, but rather that Pegasus exists in a particular worldview, the worldview of classical myth.

Thus a statement of the form is said to be true, under a particular interpretation, if there is some object in the domain of discourse of that interpretation that satisfies the predicate that the interpretation uses to assign meaning to the symbol Phil.

Thus, the statement that f is an idempotent unary operation on S is equivalent to the statement that f is an idempotent element with respect to the function composition operation ∘ on functions from S to S.

Thus, for example, the statement, " It is true that two plus two equals four ", contains no more information than the statement " two plus two equals four ", because the phrase " it is true that ..." is always implicitly there.

Thus, both the statement " Murder is bad " and the statement " Murder is good " are false, according to an error theory.

If a statement P is provable, then it is certainly impossible to prove that there is no proof of P. But even if it can be shown that no disproof of P is possible, we cannot conclude from this absence that there is a proof of P. Thus P is a stronger statement than not-not-P.

Thus the difference between the two definitions of real numbers can be thought of as the difference in the interpretation of the statement " for all ... there exists ..."

Thus the statement should not be informative.

Thus, the statement " there are no contradictions in the Principia system " cannot be proven in the Principia system unless there are contradictions in the system ( in which case it can be proven both true and false ).

Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.

Thus, even if one were to prescribe a likely and reasonable meaning to the sentence, the grammaticality of the sentence is concrete despite being the first time a person had ever uttered the statement, or any part thereof in such a combination.

Thus he made the first statement of cell theory.

Thus at least one vacuously true statement seems to actually be true.

Thus the term " syāt " should be prefixed before each proposition giving it a conditional point of view and thus removing any dogmatism in the statement.

Thus say the ( scriptures ) through the statement of sage Yajnavalkya to his wife.

Thus, although the Naskapis had never filed a formal statement of claim or similar document, except for a draft history prepared by the late Dr Alan Cooke, the parties to the JBNQA accepted the legitimacy of their claims, and they entered into an agreement-in-principle with the Naskapis in the Spring of 1977 to negotiate an agreement that would have the same principal features as the JBNQA.

Thus, the statement " n is Richardian " can not consistently be designated as either true or false.

Thus a violation of the Kelvin statement implies a violation of the Clausius statement, i. e. the Clausius statement implies the Kelvin statement.

Thus areas can be measured in square metres ( m < sup > 2 </ sup >), square centimetres ( cm < sup > 2 </ sup >), square millimetres ( mm < sup > 2 </ sup >), square kilometres ( km < sup > 2 </ sup >), square feet ( ft < sup > 2 </ sup >), square yards ( yd < sup > 2 </ sup >), square miles ( mi < sup > 2 </ sup >), and so forth.

Thus, if P is a program in L < sub > 2 </ sub > which is a minimal description of s, then InterpretLanguage ( P ) returns the string s. The length of this description of s is the sum of

Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing B by B + c < sub > 1 </ sub >-− 3 c < sub > 1 </ sub > will cause them to be renumbered from 0 through 9 and 4 through 23, respectively.

Thus this class of molecules belong to the D < sub > 2d </ sub > point group.

Thus, few drops of diamminesilver ( I ) hydroxide ( Ag ( NH < sub > 3 </ sub >)< sub > 2 </ sub > OH ) reacts with terminal alkynes signaled by formation of a white precipitate of the silver acetylide.

Thus, all the antiderivatives of x < sup > 2 </ sup > can be obtained by changing the value of C in F ( x ) = ( x < sup > 3 </ sup >/ 3 ) + C ; where C is an arbitrary constant known as the constant of integration.

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, a single " rule ," like mapping every real number x to x < sup > 2 </ sup >, can lead to distinct functions and, depending on whether the images under that rule are understood to be reals or, more restrictively, non-negative reals.

Thus, oxygen is reduced to water and the original electron acceptors NAD < sup >+</ sup > and quinone are regenerated.

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, the molecular formula of ethanol may be written in a paper in conformational, three-dimensional, full two-dimensional ( indicating every bond with no three-dimensional directions ), compressed two-dimensional ( CH < sub > 3 </ sub >– CH < sub > 2 </ sub >– OH ), separating the functional group from another part of the molecule ( C < sub > 2 </ sub > H < sub > 5 </ sub > OH ), or by its atomic constituents ( C < sub > 2 </ sub > H < sub > 6 </ sub > O ), according to what is discussed.

Thus ℵ < sub > 0 </ sub > is a regular cardinal.

Thus in Austinian terms a moral code can objectively determine what people ought to do, the law can embody whatever norms the legislature decrees to achieve social utility, but every individual remains free to choose what to do.

Thus this code number of a proof of contradition of T must be a non-standard number.

Thus in the upper block there are 2 < sup > n </ sup > − 3 codes available to the decoder that won't trigger an increase in code width.

Thus the encoder can generate 2 < sup > n </ sup > − 2 codes without triggering an increase in code width.

Thus, the most common letter in English, the letter " E ," has the shortest code, a single dot.

Thus, id's decision to protect Quake IIIs code inadvertently caused machinima creators to use more general solutions and thus widen their audience.

( Thus, they are called " macros " because a big block of code can be expanded from a small sequence of characters ).

Thus it made sense to not map the memory between programs for IPC, but instead migrate the program code being used into the local space of the program.

Thus, a person with the UPP code 675AB6 would have STR 6, DEX 7, END 5, INT 10, EDU 11 and SOC 6.

Thus the Morse code " dots " and " dashes " are audible as beeping sounds.

Thus, an interpreter might load a portable bytecode program, decode the bytecodes to generate platform-dependent threaded code, then execute threaded code without further reference to the bytecodes.

Thus, indirect code is often more compact than direct-threaded code, but the indirection also typically makes it slower, though still usually faster than bytecode interpreters.

Thus the combined size of all the instructions needed to perform a particular task, the code density, was an important characteristic of any instruction set.

Thus, while a von Neumann architecture is visible in some contexts, such as when data and code come through the same memory controller, the hardware implementation gains the efficiencies of the Harvard architecture for cache accesses and at least some main memory accesses.

Thus, the post-medieval gentlemanly code of the value of a man's honor, respect for women, and a concern for those less fortunate, is directly derived from earlier ideals of chivalry and historical forces which created it.

Thus the letters sh, sh, ch become b, b, l, i. e., Babel ( see: Atbash cipher ). This code is called the Atbash Cipher and was used to decrypt.

Thus the letter A, 12, 1 in the punched card character code, was encoded B, A, 1.

Thus code optimizations should be carefully documented ( preferably using in-line comments ), and their effect on future development evaluated.

Thus, a code smell is a driver for refactoring.

Thus a rise and a tread exactly meets this code.

However, he commented: " Only lately some well-to-do men came forward and purchased three copies of my code Mishneh Torah which they distributed through messengers ... Thus the horizon of these Jews was widened and the religious life in all communities as far as India revived.