We use the stronger statement that every odd ( antipode-preserving ) mapping h: S < sup > n-1 </ sup > → S < sup > n-1 </ sup > has odd degree.

Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S < sup > n </ sup > → ℝ < sup > n </ sup > that does not equalize on any antipodes then we can construct a map g: S < sup > n </ sup > → S < sup > n-1 </ sup > by the formula

However, as 1 + ( k + 1 ) x + kx < sup > 2 </ sup > ≥ 1 + ( k + 1 ) x ( since kx < sup > 2 </ sup > ≥ 0 ), it follows that ( 1 + x )< sup > k + 1 </ sup > ≥ 1 + ( k + 1 ) x, which means the statement is true for r = k + 1 as required.

If one statement is true in a category C then its dual will be true in the dual category C < sup > op </ sup >.

For regions in R < sup > 3 </ sup > more complicated than this, the latter statement might be false ( see Poincaré lemma ).

This was considered beneficial in that it would promote structured programming, by making it impossible to use the notorious < CODE > GO TO </ CODE > statement as before.

During the standards committee battle over whether the " minimum trip count " for the FORTRAN 77 < CODE > DO </ CODE > statement should be zero ( allowing no execution of the block ) or one ( the " plunge-ahead " < CODE > DO </ CODE >), another facetious alternative was proposed ( by Loren Meissner ) to have the minimum trip be two — since there is no need for a loop if it is only executed once.

Functions can only be defined using the single line < mathematical function of x > statement ( e. g., ).

The converse statement, namely that M < sub > p </ sub > is necessarily prime if p is prime, is false.

Thus the statement < code > IF 20 <" 30 DUCKS "</ code > is evaluated as in MUMPS.

A statement may be true for a random oracle and false for ordinary Turing machines at the same time ; for example for oracles A, IP < sup > A </ sup >≠ PSPACE < sup > A </ sup >, while IP = PSPACE.

The prime number theorem is equivalent to the statement that the nth prime number p < sub > n </ sub > is approximately equal to n ln ( n ), again with the relative error of this approximation approaching 0 as n approaches infinity.

One might expect that by the Hahn-Banach theorem for bounded linear functionals, every bounded linear functional on C < sub > c </ sub >( X ) extends in exactly one way to a bounded linear functional on C < sub > 0 </ sub >( X ), the latter being the closure of C < sub > c </ sub >( X ) in the supremum norm, and that for this reason the first statement implies the second.

An assembly language is a low-level programming language for a computer, microcontroller, or other programmable device, in which each statement corresponds to a single machine code instruction.

While he had programmed extensively in machine code in the 1950s, he was known for his low opinion of the GOTO statement in computer programming, writing a paper in 1965, and culminating in the 1968 article " A Case against the GO TO Statement ", regarded as a major step towards the widespread deprecation of the GOTO statement and its effective replacement by structured control constructs, such as the while loop.

If " hate speech " is taken to mean ethnic agitation, it is prohibited in Finland and defined in the section 11 of the penal code, War crimes and crimes against humanity, as publishing data, an opinion or other statement that threatens or insults a group on basis of race, nationality, ethnicity, religion or conviction, sexual orientation, disability, or any comparable basis.

DikuMUD had a key influence on the early evolution of the MMORPG genre, with EverQuest ( created by avid DikuMUD player Brad McQuaid ) displaying such Diku-like gameplay that Verant developers were made to issue a sworn statement that no actual DikuMUD code was incorporated.

All such licenses usually have additional restrictions such as a requirement to preserve the name of the authors and a copyright statement within the code.

* The statement, which conditionally executes a block of code, along with and ( a contraction of else-if ).

* The statement, which executes a block of code as long as its condition is true.

* The statement, which allows exceptions raised in its attached code block to be caught and handled by clauses ; it also ensures that clean-up code in a block will always be run regardless of how the block exits.

* The statement, which executes a block of code and attaches its local namespace to a class, for use in object-oriented programming.

* The statement ( from Python 2. 5 ), which encloses a code block within a context manager ( for example, acquiring a lock before the block of code is run, and releasing the lock afterwards ).

Structured programming is a programming paradigm aimed on improving the clarity, quality, and development time of a computer program by making extensive use of subroutines, block structures and for and while loops – in contrast to using simple tests and jumps such as the goto statement which could lead to " spaghetti code " which is both difficult to follow and to maintain.

Self-modifying code can also be used to affect control flow through its side effects, but does not usually involve an explicit control flow statement ( an exception being the ALTER verb in COBOL ).

Interpreting code is slower than running the compiled code because the interpreter must analyze each statement in the program each time it is executed and then perform the desired action, whereas the compiled code just performs the action within a fixed context determined by the compilation.

The oath remains unchanged since its adoption in 1984 and consists of a statement of the code, followed by a resolution to live honorably:

If the child exited with a zero return code, sh would look for a then clause ( a separate statement, but often written joined on the same line with a semicolon ) and run that nested block.

For instance, a SQL statement could be inserted as text within C source code, and during compilation it would be converted into a custom format that directly called a function within a library that would pass the statement into the SQL system.

< nowiki >< nowiki ></ nowiki > Sunday Express 1976-03-21: 1 / 2 .</ ref > Three years later, when True Whig partisans petitioned him to seek the amendment's repeal, he replied that their statement would only encourage him in his previous position: " I will serve my country as long as I have life.

The primary blocking consisted of a wall of cemented limestone blocks, plastered and stamped with the seal of the Royal Necropolis ( with the jackal and nine captives motif ).< ref name =" reeves p. 42 "> Reeves, C. N., < cite > Valley of the Kings </ cite > ( Kegan Paul, 1990 ) p. 42 </ ref > Weigall later stated that a fragment of Tutankhamun's seal had been recovered from this original blocking .< ref > Weigall, A. E. P. B., < cite > The Treasury of Ancient Egypt </ cite > ( Rand McNally and Company, 1912 ) p. 208 </ ref > However, his statement is not corroborated by any of the other reports dating from the initial discovery, leaving Weigall's claim open to question .< ref > Davis, T. M., < cite > The Tomb of Queen Tiyi </ cite >, ( KMT Communications, 1990 ) p. vi .</ ref >< ref > Bell, M. R., < cite >" An Armchair Excavation of KV 55 ", JARCE 27 ( 1990 )</ cite > p. 136 </ ref >

This statement will generate a new definition of < var > y </ var >, < var > y </ var >< sub > 3 </ sub >, by " choosing " either < var > y </ var >< sub > 1 </ sub > or < var > y </ var >< sub > 2 </ sub >, depending on which arrow control arrived from:

< ol >< li > from " Mainstream Science on Intelligence " ( 1994 ), an editorial statement by fifty-two researchers:

In 1975 Bok coauthored the statement Objections to Astrology ( The Humanist, 1975 ),< ref >< nowiki > http :// www. americanhumanist. org / about / astrology. html </ nowiki > which was endorsed by 186 professional astronomers, astrophysicists, and other scientists, including nineteen winners of the Nobel Prize.

Bateson goes on to give the general characteristics of such a relationship :< ol style =" list-style-type: lower-alpha ;">< li > When the victim is involved in an intense relationship ; that is, a relationship in which he feels it is vitally important that he discriminate accurately what sort of message is being communicated so that he may respond appropriately ;</ li >< li > And, the victim is caught in a situation in which the other person in the relationship is expressing two orders of message and one of these denies the other ;</ li >< li > And, the victim is unable to comment on the messages being expressed to correct his discrimination of what order of message to respond to: i. e., he cannot make a metacommunicative statement .</ li ></ ol >

The assumption m ≥ n in the algorithm statement is necessary, as otherwise the matrix J < sub > r </ sub >< sup > T </ sup > J < sub > r </ sub > is not invertible and the normal equations cannot be solved ( at least uniquely ).

The two train services that disrupted on the NSL that took place on 15 and 17 December 2011 caused major disruptions ever since SMRT started operation for 24 years .< ref >< ref name =" S < sub > 2 </ sub > Nd Update – SMRT statement: Service disruption on North-South Line ( Northbound ): Marina Bay Station to Bishan Station "> All MRT stations on the North South Line and East West Line were further closed due to checks on all trains and tracks to be carry out.

" An 1875 statement signed by nine witnesses said that Lowerie's grandfather was of Tuscarora descent, as were several of the women in the area .< ref >< Mary Normant, The Lowry History, 1875 </ ref > Another account said of Pop Oxendine ( a member of the gang ) that " like the rest ...... he had the Tuscarora Indian blood in him ".

Unequal fissions are energetically more favorable because this allows one product to be closer to the energetic minimum near mass 60 u ( only a quarter of the average fissionable mass ), while the other nucleus with mass 135 u is still not far out of the range of the most tightly bound nuclei ( another statement of this, is that the atomic binding energy curve is slightly steeper to the left of mass 120 u than to the right of it ).

: Marking the centenary of the passing of Bahá ' u ' lláh, this statement is a review of his life and work.

This statement has made many people unsure about using K < sub > u </ sub >- band ( 11 – 18 GHz ) in Indonesia.

issued a statement directed to their gay fans: " When t. A. T. u.

For instance, a statement " I haven't < u > ever </ u > owed < u > anything </ u > to < u > anyone </ u >" would be rendered as es nekad nevienam neko neesmu bijis parādā.

The only certainty in this regard is ` Attar's own statement that he once met him .< ref > Ta < u > d </ u > kerat al-Awlīya ; pp. 1, 6, 21 </ ref >

Bahá ' u ' lláh, who claims to be and is widely recognized as being that figure, in the Kitáb-i-Aqdas confirms the Báb's statement and further ordains his final resting-place as the Qiblih.

Wales based u. k alternative rock band ' Samoans ', feature no actual people of a Samoan descent, the name is understood to be an ironic statement due to their pale complexion.

The designated charger is then given 60 seconds to progress his or her way up the six levels of the board by choosing one of the five spaces on a level and correcting a blooper, a factual statement with an incorrect word creating a pun ( e. g., " The B & O was the first American passenger < u > smell </ u >", with train as the correct answer ).

The Azalis, those Babis who did not accept Bahá ' u ' lláh, objected to Bahá ' u ' lláh's statement, and shortly after Bahá ' u ' lláh's claim first started to attract attention, Bahá ' í historians report Subh-i-Azal made a claim to the title.