Consider a number n > 0 in base b ≥ 2, where it is written in standard notation with k + 1 digits a < sub > i </ sub > as:

Consider a n < font face =" Arial " size =" 2 "> x </ font > n matrix A.

( Consider 1 / 0, which is defined with the value of infinity, vs. 0 / 0, which is undefined.

Geometric arrangement for Fresnel's calculation Consider the case of a point source located at a point P < sub > 0 </ sub >, vibrating at a frequency f. The disturbance may be described by a complex variable U < sub > 0 </ sub > known as the complex amplitude.

< li > Consider the group ( Z < sub > 6 </ sub >, +), the integers from 0 to 5 with addition modulo 6.

Again we start with a C < sup >∞</ sup > manifold, M, and a point, x, in M. Consider the ideal, I, in C < sup >∞</ sup >( M ) consisting of all functions, ƒ, such that ƒ ( x ) = 0.

Consider the vectors e < sub > 1 </ sub > = ( 1, 0, 0 ), e < sub > 2 </ sub > = ( 0, 1, 0 ) and e < sub > 3 </ sub > = ( 0, 0, 1 ).

Consider the function f, piecewise defined by f ( x ) = – 1 for x < 0 and f ( x ) = 1 for x ≥ 0.

We say that the number x is a periodic point of period m if f < sup > m </ sup >( x ) = x ( where f < sup > m </ sup > denotes the composition of m copies of f ) and having least period m if furthermore f < sup > k </ sup >( x ) ≠ x for all 0 < k < m. We are interested in the possible periods of periodic points of f. Consider the following ordering of the positive integers:

Consider for instance the open unit disc, a non-compact Riemann surface without boundary, with curvature 0 and with Euler characteristic 1: the Gauss – Bonnet formula does not work.

Consider the theory obtained by adding a new constant symbol ε to the language and adjoining to Σ the axiom ε > 0 and the axioms ε < 1 / n for all positive integers n. Clearly, the standard real numbers R are a model for every finite subset of these axioms, because the real numbers satisfy everything in Σ and, by suitable choice of ε, can be made to satisfy any finite subset of the axioms about ε.

Consider for instance the map f: ( 0, 1 ) → R < sup > 2 </ sup > with f ( t )

Consider the following swap in which Party A agrees to pay Party B periodic fixed interest rate payments of 8. 65 %, in exchange for periodic variable interest rate payments of LIBOR + 70 bps ( 0. 70 %) in the same currency.

Proof: Consider the elements ( 1, 0 ) and ( 0, 1 ).

Consider the ring generated by pairs ( X, V ) where V is a smooth vector bundle on the compact smooth oriented manifold X, with relations that the sum and product of the ring on these generators are given by disjoint union and product of manifolds ( with the obvious operations on the vector bundles ), and any boundary of a manifold with vector bundle is 0.

Listen to what Mr. Johnston has to say: `` Consider the savage wounds that isolationism would inflict.

Consider this table: 1.

Consider what you have to earn to be able to spend the $3,000 and your building time is well worth it.

Consider it as a standby setup, at negligible cost, for those emergencies when the furnace quits, a blizzard holds up fuel delivery, or for cool summer mornings or evenings when you don't want to start up your whole heating plant.

Consider what you can afford to spend and what your goals are before setting up or revamping your employee benefit program.

Consider installing supplemental serving lines in production areas.

Consider adopting a system of holidays in which time off is granted with an eye to minimum inconvenience to the operation of the plant.

Consider using vending machines rather than subsidized cafeterias.

Consider the equipment needed to protect this many from the weather, to make their cooking easy and their sleeping comfortable.

Consider a shear field with a height of H and a cross-sectional area of A opposed by a manometer with a height of H ( referred to the same base as H ) and a cross-sectional area of A.

Consider couples visiting an art museum.

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.

Consider the traditional `` four fields '' of philosophy: logic, ethics, epistemology and esthetics.

Consider what follows from the positivist view.

Consider the four monks who figure prominently in the action: Pimen, Varlaam, Missail and the Jesuit Rangoni.

Consider the process illustrated in Fig. 2.1, consisting of R distinct stages.

Consider what happened during World War 1,, when the Protestant churches united to push the Prohibition law through Congress.

Consider opportunity.

Consider the tense system.

Consider the sample ( 4, 7, 13, 16 ) from an infinite population.

Consider the assembly of a car: assume that certain steps in the assembly line are to install the engine, install the hood, and install the wheels ( in that order, with arbitrary interstitial steps ); only one of these steps can be done at a time.

Consider the first equation.

* Consider a set with three elements, A, B, and C. The following operation:

Consider the graph of the equation y = 1 / x shown to the right.

Consider, for instance, particles suspended in a viscous fluid in a gravitational field.

Consider a 35 mm camera with a lens having a focal length of.

Consider another application similar to the one above with the 12 mm pin.