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Every completely multiplicative function is a homomorphism of monoids and is completely determined by its restriction to the prime numbers.
Some Related Sentences
Every and completely
Every now and then an atom is replaced by a completely different atom ( and this could be as few as one in a million atoms ).
Every family large enough to completely consume a young lamb or wild goat was required to offer one for sacrifice at the Jewish Temple on the afternoon of the 14th day of Nisan ,() and eat it that night, which was the 15th of Nisan ().
* Every locally compact regular space is completely regular, and therefore every locally compact Hausdorff space is Tychonoff.
Every isolated unstable black hole decays rapidly to a stable black hole ; and ( modulo quantum fluctuations ) stable black holes can be completely described ( in a Cartesian coordinate system ) at any moment in time by these eleven numbers:
Every Ophrys orchid has its own pollinator insect and is completely dependent on this species for its survival.
He has gained a reputation of being cursed due to several notorious strokes of bad luck: Every team he was assigned to would be completely annihilated on their third mission together, save for Sanders himself.
Every hour or so, a 10 – 20 minute ' word war ' is held in which the entire room falls almost completely silent with concentration, save for the sound of keystrokes.
Every day, day-by-day, without fail she would rub herself against the walls, till her clothes became thinner, and thinner till she completely wore it out.
* Every atom in the ring must have a p orbital, which overlaps with p orbitals on either side ( completely conjugated ).
Every time he tried attacking major WWF stars such as The Rock or Kurt Angle, he would run into a wall, statue, milk truck, or just completely miss and trip over his boots.
Every variation of the Alpha-Bits line is now made completely with whole grains and three grams of fiber per serving.
Every plane B that is completely orthogonalTwo flat subspaces S < sub > 1 </ sub > and S < sub > 2 </ sub > of dimensions M and N of a Euclidean space S of at least M + N dimensions are called completely orthogonal if every line in S1 is orthogonal to every line in S2.
Every and multiplicative
Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.
Every nonzero real number has a multiplicative inverse ( i. e. an inverse with respect to multiplication ) given by ( or ).
Every prime power ( except powers of 2 ) has a primitive root ; thus the multiplicative group of integers modulo p < sup > n </ sup > ( or equivalently, the unit group of the ring ) is cyclic.
Every and function
Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.
Every contraction mapping is Lipschitz continuous and hence uniformly continuous ( for a Lipschitz continuous function, the constant k is no longer necessarily less than 1 ).
Every effectively calculable function ( effectively decidable predicate ) is general recursive italics
Every bijective function g has an inverse g < sup >− 1 </ sup >, such that gg < sup >− 1 </ sup > = I ;
Every entire function can be represented as a power series that converges uniformly on compact sets.
Every holomorphic function can be separated into its real and imaginary parts, and each of these is a solution of Laplace's equation on R < sup > 2 </ sup >.
Every time another object or customer enters the line to wait, they join the end of the line and represent the “ enqueue ” function.
Every type that is a member of the type class defines a function that will extract the data from the string representation of the dumped data.
Every output of an encoder can be described by its own transfer function, which is closely related to the generator polynomial.
Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.