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Page "Equivalence class" ¶ 23
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Any and function
Any cryptographic hash function, such as MD5 or SHA-1, may be used in the calculation of an HMAC ; the resulting MAC algorithm is termed HMAC-MD5 or HMAC-SHA1 accordingly.
Any compression algorithm can be viewed as a function that maps sequences of units ( normally octets ) into other sequences of the same units.
The blitter's block copying mode takes zero to three data sources in memory, called A, B and C, performs a programmable boolean function on the data sources and writes the result to a destination area, D. Any of these four areas can overlap.
Any real-valued differentiable function, H, on a symplectic manifold can serve as an energy function or Hamiltonian.
Any non-constant algebraic function of a single variable yields a transcendental value when applied to a transcendental argument.
Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.
Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and / or its surrounding.
Any poles on the imaginary axis have real strictly positive residues, and similarly at any zeros on the imaginary axis, the function has a real strictly positive derivative.
Any building requires a certain amount of internal infrastructure to function, which includes such elements like heating / cooling, power and telecommunications, water and wastewater etc.
Any such function is called a Urysohn function for A and B.
Any function can be restricted to a subset of its domain.
Any such K is referred to as a Lipschitz constant for the function ƒ.
Any impairment which limits the physical function of limbs or fine or gross motor ability is a physical disability.
* Any polynomial ( real or complex ) is an analytic function.
Any Taylor series for this function converges not only for x close enough to x < sub > 0 </ sub > ( as in the definition ) but for all values of x ( real or complex ).
* Any analytic function is smooth, that is, infinitely differentiable.
Any real analytic function on some open set on the real line can be extended to a complex analytic function on some open set of the complex plane.
" Any sequence of numbers that may be modeled by a mathematical function can be considered a pattern.
Any such satisficing problem can be formulated as an ( equivalent ) optimization problem using the Indicator function of the satisficing requirements as an objective function.
Any particular Boolean function can be represented by one and only one full disjunctive normal form, one of the two canonical forms.

Any and itself
** Any union of countably many countable sets is itself countable.
* Any commutative ring R is an algebra over itself, or any subring of R.
Any such totality would itself have to be a set, thus lying somewhere within the hierarchy and thus failing to contain every set.
# Any experience which is inconsistent with the organization of the structure of the self may be perceived as a threat, and the more of these perceptions there are, the more rigidly the self structure is organized to maintain itself.
:* Any total order on X has exactly one equivalence class, X itself, because x ~ y for all x and y ;
Any subset of R < sup > n </ sup > ( with its subspace topology ) that is homeomorphic to another open subset of R < sup > n </ sup > is itself open.
Any rule can be changed with varying degrees of difficulty, including the core rules of the game itself.
Any measurable subset of a null set is itself a null set.
Any given procedure might be called at any point during a program's execution, including by other procedures or itself.
Any topological space which is itself finite or countably infinite is separable, for the whole space is a countable dense subset of itself.
# Any tool should be useful in the expected way, but a truly great tool lends itself to uses you never expected.
Any document element could be given new " methods " ( capabilities ), and could respond to changes in the content or structure of the document itself.
Any energy released by the explosion not radiated away in the burst itself takes the form of matter or energy moving outward at nearly the speed of light.
Any group can be seen as a category with a single object in which every morphism is invertible ( for every morphism f there is a morphism g that is both left and right inverse to f under composition ) by viewing the group as acting on itself by left multiplication.
Any hardware component, including the TC hardware itself, has the potential to fail, or be upgraded and replaced.
Any country has a right to defend itself from terror.
Any ‘ confused person ’ may continue to run on cycles meeting bad spirits or even Satan ( Ekwensu ) itself.
* Any number raised by the exponent 1 is the number itself.
Any entity from the real or virtual world that lends itself to dramatic interpretation may be taken up as a subject.
Any function passed as an argument to f is invoked with itself as an argument, and thus in any use of that argument is indirectly referring to itself.
Any class that needs a " polymorphic constructor " capability derives itself from the abstract base class, and implements the clone () operation.
Any of these will result in some power to the solenoid, but not enough to hold the heavy contacts closed, so the starter motor itself never spins, and the engine does not start.

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