Lemma: Every sequence

Lemma: Any linear code is permutation equivalent to a code which is in standard form.

Lemma 1: For all codewords, in a Walsh – Hadamard code,,, where represent the bits in in positions and respectively, and represents the bit at position.

The fact that there can not be any limit points of the set except in closed intervals follows from the argument used in Lemma 1, namely, that near any tangent point in the C-plane the curves C and Af are analytic, and therefore the difference between them must be a monotone function in some neighborhood on either side of the tangent point.

In this way, Yoneda's Lemma provides a complete classification of all natural transformations from the functor Hom ( A ,-) to an arbitrary functor F: C → Set.

Lemma: Let A ∈ C < sup > n × n </ sup > be a complex-valued matrix, ρ ( A ) its spectral radius and ||·|| a consistent matrix norm ; then, for each k ∈ N:

Lemma 1.

Lemma 2.

Lemma 3.

otherwise by Lemma 1 the component would extend beyond these points.

Further, we see by Lemma 2 that the multiplicity of F can only change at a tangent point, and at such a point can only change by an even integer.

Lemma 4.

* Lemma A Banach space X is reflexive if and only if the natural pairing on X × X ′ is perfect.

Lemma.

However, this idea can be understood as a basis for the following proof of the Lemma.

We have proved that φ is either satisfiable or refutable, and this concludes the proof of the Lemma.

As shown by the Lemma above, we only need to prove our theorem for formulas φ in R of degree 1. φ cannot be of degree 0, since formulas in R have no free variables and don't use constant symbols.

Lemma 1.

Lemma 2.

Pavel Samuilovich Urysohn, Pavel Uryson () ( February 3, 1898, Odessa – August 17, 1924, Batz-sur-Mer ) was a Jewish mathematician who is best known for his contributions in the theory of dimension, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology.

( The same applies to Zorn's Lemma.

The well ordering theorem follows easily from Zorn's Lemma.

He also gives starting at Lemma 4 and Proposition 40 ) the theory of the motions of comets ( for which much data came from John Flamsteed and from Edmond Halley ), and accounts for the tides, attempting quantitative estimates of the contributions of the Sun and Moon to the tidal motions ; and offers the first theory of the precession of the equinoxes.

* Franz Miklosich ( Lemma by Katja Sturm-Schnabl, p. 186-193 ) in: Marija Mitrović, Die Geschichte der slowenischen Literatur von den Anfängen bis zur Gegenwart.

Conditions for Lemma 2 shall hold for all factor, any violation will result in satisfying the condition of Lemma 1 whereby the result has been proven.

Ngô Bảo Châu proved an auxiliary but difficult statement, the so-called " Fundamental Lemma ", originally conjectured by Langlands.

* Singleton bound, used in coding theory

Singleton bound ===

The Singleton bound is that the sum of the rate and the relative distance of a block code cannot be much larger than 1:

In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude bound on the size of a block code with block length, size and minimum distance.

Then the Singleton bound states that

Block codes that achieve equality in Singleton bound are called MDS ( maximum distance separable ) codes.

* Singleton bound

* Bell, R. & Singleton, L. ( 1974 ): A sighting of the Piopio or Native Thrush.

* 2nd World Rogaining Championship ( 1996 ): Mt Singleton, Western Australia, 640 participants in 271 teams

Despite having already created a substantial amount of new game code — essentially all the above engines --, Singleton was involved in numerous other game projects at the time and thus put the game on hiatus.

* Earlier graduates include J. C. R. Licklider, pioneer in artificial intelligence ; Charles Nagel, founder of the U. S. Chamber of Commerce ; Julian Hill, co-inventor of nylon ; Clyde Cowan, co-discoverer of the neutrino ; James R. Thompson, Governor of Illinois ; David R. Francis, Governor of Missouri ; William H. Webster, former Director of the FBI ; Edward Singleton Holden, President of the University of California ; Nathan O. Hatch, president of Wake Forest University ; Thomas Lamb Eliot, President of Reed College ; and Abram L. Sachar, founding President of Brandeis University.

* C. T. Singleton, Jr., ( 1905-1977 ), American admiral

* Singleton, Richard C. ( 1967 ).

Singleton, C. C.

* Straits, Bruce C. and Singleton, Royce A.

< td bgcolor =# DDEEFF align = center > C G Singleton

The movie Anger Management starts off with a confrontation between Adam Sandler's character David " Dave " Buznik and an air marshal ( played by Isaac C. Singleton Jr ).

* R C Singleton ( 1847 – 1851 )

" In addition, the Core of Cybertron, ( Isaac C. Singleton, Jr .) is a homage to Primus.

* Isaac C. Singleton, Jr .-Lurtz

The trial began at the Old Bailey on 20 July 1931 before Mr Justice Wright, with Sir William Jowitt, D. N. Pritt and Eustace Fulton for the prosecution, Sir John Simon, J. E. Singleton and Wilfred Lewis for Lord Kylsant, and Hastings, Stuart Bevan, Frederick Tucker and C. J. Conway for John Morland.

In 1969, Mercury Records label producer Shelby Singleton – noted for producing the Ray Stevens ' hit " Ahab The Arab " in 1962, and later Jeannie C. Riley's 1968 hit single " Harper Valley PTA " on his Nashville based Plantation Records label – purchased the Sun label from Phillips.