Another equivalent axiom only considers collections X that are essentially powersets of other sets:

Another advantage with analog signals is that their processing may be achieved more simply than with the digital equivalent.

Another definition of asymmetric makes asymmetry equivalent to antisymmetry plus irreflexivity.

Another Vala, Aulë, creates the Dwarf race as an act of subcreation that honoured Eru Ilúvatar ( The equivalent of God in Tolkien's writings ), and which Eru accepted and made real, just as Niggle's Tree was made real.

Another matrix string theory equivalent to Type IIB string theory was constructed in 1996 by Ishibashi, Kawai, Kitazawa, and Tsuchiya.

Another equivalent definition of the rank of a matrix is the greatest order of any non-zero minor in the matrix ( the order of a minor being the size of the square sub-matrix of which it is the determinant ).

Another feature is the NET ( Null End Tag ) construction:, which is structurally equivalent to.

Another formalism mathematically equivalent to regular expressions, Finite automata are used in circuit design and in some kinds of problem-solving.

Another equivalent definition is

Another prominent opponent of Bligh, Macarthur's ally Thomas Jamison, was made the colony's Naval Officer ( the equivalent of Collector of Customs and Excise ).

Another report suggested that in 1669, Tavernier sold this large blue diamond along with approximately one thousand other diamonds to King Louis XIV of France for 220, 000 livres, the equivalent of 147 kilograms of pure gold.

Another example is al-Tusi's son, Sadr al-Din ( sometimes known as " Pseudo-Tusi "), who wrote a book on the subject in 1298, based on al-Tusi's later thoughts, which presented another hypothesis equivalent to the parallel postulate.

Another place is called the typical thirteenth Pratum magnum, a large open area destined to the market ( equivalent to today's Piazza Trento e Trieste ).

Another equivalent measure of proximity to instability is the phase margin.

Another roughly equivalent title and area in medieval Eastern Europe were those of ban ( bojan, vojin or bayan ) and banate.

* Another variation includes being sent to procure a " long weight " or " long stand ," the idea being that the dupe will reach the shop ( or equivalent source of the mythical object ) and place the request.

Another equivalent version is

Another divide and conquer algorithm with a single subproblem is the Euclidean algorithm to compute the greatest common divisor of two numbers ( by reducing the numbers to smaller and smaller equivalent subproblems ), which dates to several centuries BC.

Another equivalent formula for the area, which more closely resembles Heron's formula, is

Another language game, " Fannee Doolee ," centers around a character who likes any person, place, thing or concept with double letters in it but hates its non-double-lettered equivalent, e. g., " Fannee Doolee likes sweets but hates candy.

Another equivalent definition with the advantage of brevity is

Another way of putting this is that a phase angle of, say, 5 ° is considered to be completely equivalent to an angle of 365 °.

Another rearrangement shows that the Jacobi identity is equivalent to the following identity between the operators of the adjoint representation:

Another consideration is that due to the fact that territory controlled by Tang central authority was diminished by the equivalent of several of the northern provinces, something like a quarter of the remaining population no longer remained within the imperial revenue system.

Another method of assuring a clean hole is to first drill a small pilot hole all the way through, then drill half way with the dimensional bit, turn the piece over, and finish from the other side.

Another way to remove small objects from the eye was to have the person look cross-eyed ; ;

Another way is merely " one of the many modern substitutes for love, ... nothing but the urge to turn away from oneself and to lose oneself in other people ’ s business.

Another situation is where appeal is by way of " re-hearing ".

Another example is about, which has three different ways of signing it ; these are the standard way and two regional variations ( Atlantic and Ontario ).

Another way of making the point is that if the Platonic world were to disappear, it would make no difference to the ability of mathematicians to generate proofs, etc., which is already fully accountable in terms of physical processes in their brains.

Another line of defense is to maintain that abstract objects are relevant to mathematical reasoning in a way that is non causal, and not analogous to perception.

Another way to state this is that the emitting object may have a transverse velocity with respect to the observer, but any light beam emitted from it which reaches the observer, cannot, for it must have been previously emitted in such a direction that its transverse component has been " corrected " for.

Another way to define the Bessel functions is the Poisson representation formula and the Mehler-Sonine formula:

Another way of putting the argument is to say computational computer programs can pass the Turing test for processing the syntax of a language, but that semantics cannot be reduced to syntax in the way Strong AI advocates hoped: processing semantics is conscious and intentional because we use semantics to consciously produce meaning by what we say.

Another way of computing this derivative is to view the composite function as the composite of and h. Applying the chain rule to this situation gives:

Another way of proving the chain rule is to measure the error in the linear approximation determined by the derivative.

Another way of writing the chain rule is used when f and g are expressed in terms of their components as and.

Another way to eat couscous is as a dessert ; it is prepared with dates, sesame, and pure honey, and locally referred to as " maghrood ".

Another way to represent coordinate transformations in Cartesian coordinates is through affine transformations.

Another way to define Chomsky normal form ( e. g., Hopcroft and Ullman 1979, and Hopcroft et al.

Another way a diatomic molecule can move is to have each atom oscillate — or vibrate — along a line ( the bond ) connecting the two atoms.

Another way is IPTV, that is receiving TV via Internet Protocol, relying on Digital Subscriber Line ( DSL ) or optical cable line.

Another way is by their application area, for example: accounting, music compositions, movies, banking, manufacturing, or insurance.

Another way to represent results is in DMIPS / MHz, where DMIPS result is further divided by CPU frequency, to allow for easier comparison of CPUs running at different clock rates.

Another way of looking at the DFT is to note that in the above discussion, the DFT can be expressed as a Vandermonde matrix:

Another way of looking at the deal as the excess return achieved ( over the risk-free rate ) is ( 14. 5 %- 5. 0 %)/( 100 %+ 5 %) or approximately 9. 0 % ( still very respectable ).

Another way of putting this is to say a perfectly competitive market exists when every participant is a " price taker ", and no participant influences the price of the product it buys or sells.