This guarantees for any partition of a set X the existence of a subset C of X containing exactly one element from each part of the partition.

So assume ƒ is differentiable at 0, as a function of two real variables from Ω to C. This is equivalent to the existence of two complex numbers and ( which are the partial derivatives of ƒ ) such that we have the linear approximation

The suffix “ ene ” indicates that each C atom is covalently bonded to three others ( instead of the maximum of four ), a situation that classically would correspond to the existence of bonds involving two pairs of electrons (“ double bonds ”).

Applying the completeness theorem to this result, gives the existence of a model of T where the formula C < sub > T </ sub > is false.

For example, P. Schuyler Miller called Arthur C. Clarke's 1961 novel A Fall of Moondust hard SF, and the designation remains valid even though a crucial plot element, the existence of deep pockets of " moondust " in lunar craters, is now known to be incorrect.

A defendant who admits the existence of the contract in his pleadings, under oath in a deposition or affidavit, or at trial, may not use the defense under the U. C. C.

The 423-carat ( 85 g ) Logan sapphire in the National Museum of Natural History, in Washington, D. C., is one of the largest faceted gem-quality blue sapphires in existence.

The existence theorem for limits states that if a category C has equalizers and all products indexed by the classes Ob ( J ) and Hom ( J ), then C has all limits of type J.

If C is a complete category, then, by the above existence theorem for limits, a functor G: C → D is continuous if and only if it preserves ( small ) products and equalizers.

He later postulated the existence of other essential nutrients, which became known as B < sub > 1 </ sub >, B < sub > 2 </ sub >, C, and D. In 1936 he determined the molecular structure of thiamin, though he was not the first to isolate it.

For instance, the existence of pointers in C and C ++ makes it difficult to optimize array accesses ( see alias analysis ).

J. J. C. Smart, a proponent of this view, uses the term " tenselessness " to describe the simultaneous existence of past, present, and future.

were champions of Cornwall in 1955 / 56 and have been in existence over a hundred years ; their most notable player was Harry Cann who was goalkeeper for Plymouth Argyle F. C .. Until the 1930s there were two golf courses and a few tennis courts: neither golf course reopened in the postwar period.

Another theory explaining the existence of the seacoast in Bohemia offered by C. H.

The C shell implements a 32-bit integer expression grammar with operators borrowed from C but with a few additional operators for string comparisons and filesystem tests, e. g., testing for the existence of a file.

Portland's compulsory education is a result of the existence of Gregory-Portland Independent School District made up of W. C. Blunt ( K-4 ), T. M. Clark Elementary School ( K-4 ), East Cliff Elementary School ( K-4 ), Gregory-Portland Intermediate School ( 5-6 ), and Gregory-Portland High School ( 9-12 ).

The original authors ( Andrew C. Oliver and Marc Johnson ) also noted the existence of the Hawaiian poi dish, made of mashed taro root, which had similarly derogatory connotations.

In 1977 the N. C. General Assembly repealed the laws authorizing its existence, though it would not be until 2003 that the involuntary sterilization laws that underpinned the Board's operations were repealed.

We first assume the existence of a set C of column names, examples of which are " name ", " author ", " address " et cetera.

Evidence for ( or against ) the existence of diatomic astatine ( At < sub > 2 </ sub >) is sparse and inconclusive.

Some sources state that At < sub > 2 </ sub > does not exist, or at least has never been observed, while other sources assert or imply its existence.

( 2006 ): Particle listings – Θ < sup >+</ sup > and in 2008, considered evidence to be overwhelmingly against the existence of the reported pentaquarks.

As usual for objects defined by universal mapping properties, this shows the uniqueness of the abelianization G < sup > ab </ sup > up to canonical isomorphism, whereas the explicit construction G → G / shows existence.

Despite this opinion among researchers, evidence has accumulated that supports the existence of complex biological effects of weaker non-thermal electromagnetic fields, ( including weak ELF magnetic fields, although the latter does not strictly qualify as EM radiation < ref >), and modulated RF and microwave fields.

One of his other findings resulted from measurements of the dependence of the intensity of the electric photo current on the gas pressure, where he found the existence of an optimal gas pressure P < sub > m </ sub > corresponding to a maximum photocurrent ; this property was used for a creation of solar cells.

Grand unification would imply the existence of an electronuclear force ; it is expected to set in at energies of the order of 10 < sup > 16 </ sup > GeV, far greater than could be reached by any possible Earth-based particle accelerator.

His most original contribution is the elementary solution he provided for the Riemann – Hilbert problem f < sub >+</ sub > = g f < sub >−</ sub > about the existence of a differential equation with given monodromy group.

Note that the requirement d ( T ( x ), T ( y )) < d ( x, y ) for all unequal x and y is in general not enough to ensure the existence of a fixed point, as is shown by the map T: < nowiki >

< p > Eichmann's defense lawyer argued that Israel didn't have jurisdiction on account of Israel not having come into existence until 1948.

For example, Durandal's rampancy is believed to be caused by his mistreatment at the hands of his handler, Bernard Strauss, as well as his limited existence in opening and closing the Marathon < nowiki >'</ nowiki > s doors.

The existence of a morphism between R → S < sub > 1 </ sub > and R → S < sub > 2 </ sub > implies that S < sub > 1 </ sub > is at least as efficient a solution as S < sub > 2 </ sub > to our problem: S < sub > 2 </ sub > can have more adjoined elements and / or more relations not imposed by axioms than S < sub > 1 </ sub >.

Calculations using a quantum-tunneling model predict the existence of several isotopes of ununseptium with alpha-decay half-lives up to over 10 ms, culminating at < sup > 296 </ sup > Uus ( the research ends on < sup > 303 </ sup > Uus ).

The particle physics community as a whole did not view their existence as likely in 2006 ,< ref name = PDGPentaquarks2006 > W .- M. Yao et al.

)</ ref > In a September 2009 interview with Examiner. com, Strassman described the effects on participants in the study: " Subjectively, the most interesting results were that high doses of DMT seemed to allow the consciousness of our volunteers to enter into non-corporeal, free-standing, independent realms of existence inhabited by beings of light who oftentimes were expecting the volunteers, and with whom the volunteers interacted.

Other types of hadron may exist, such as tetraquarks ( or, more generally, exotic mesons ) and pentaquarks ( exotic baryons ), but no current evidence conclusively suggests their existence .< ref name = PDGPentaquarks2006 > W .- M. Yao et al.

The earliest Laos legal document ( and the earliest sociological evidence about the existence of the Lao people ) is known as " the laws of Khun Borom " ( also spelled " Khun Bulom "), still preserved in manuscript form .< ref >

One of the suspected mechanisms behind the autoimmune phenomenon is the existence of microchimerism, i. e. fetal cells circulating in maternal blood, triggering an immune reaction to what is perceived as " foreign " material .< ref name = Bianchi >

My most sincere friend, my confidant, my very existence, my Sultan, my one and only love .</ br >

:< nowiki >*</ nowiki > The existence of these elements has been claimed and generally accepted, but not yet acknowledged by the IUPAC.

The universe is commonly defined as the totality of existence ,< ref >

They denied the existence of substantial matter and proposed that movement consisted of momentary flashes of a stream of energy .< ref > Stcherbatsky, F. Th.