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Page "Compactness theorem" ¶ 7
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Consider and theory
Consider the approach we would take classically-we pick one block at random, and then perform a normal search through the rest of the blocks ( in set theory language, the compliment ).
Consider the language of set theory with extra constant symbols c < sub > 1 </ sub >, c < sub > 2 </ sub >, ... for each positive integer.
They find that orienting strategies should be understood as metatheories: " Consider the very large proportion of sociological theory that is in the form of metatheory.
Consider a social decision model of the kind used in the theory of social choice ( such as used in stating Arrow's theorem ).
Consider a finite group permuting those indeterminates over K. By standard Galois theory, the set of fixed points of this group action is a subfield of, typically denoted.
Consider a classically parity-invariant gauge theory whose gauge group G has dual coxeter number h in 3-dimensions.

Consider and obtained
Consider a polygon P and a triangle T, with one edge in common with P. Assume Pick's theorem is true for both P and T separately ; we want to show that it is also true to the polygon PT obtained by adding T to P. Since P and T share an edge, all the boundary points along the edge in common are merged to interior points, except for the two endpoints of the edge, which are merged to boundary points.
Consider now the finite approximations to the Wallis product, obtained by taking the first k terms in the product:

Consider and by
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 a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.
Consider on K the metric induced by the uniform distance.
Consider a car's cruise control, which is a device designed to maintain vehicle speed at a constant desired or reference speed provided by the driver.
* Consider Phlebas, a novel by Iain M Banks, contains depictions of a tribe known as the Eaters, who repeatedly engage in coprophagia.
Consider for instance the sequence defined by and.
Consider, friend, as you pass by: As you are now, so once was I.
Consider a rectangular area a by b, and any common divisor c that divides both a and b exactly.
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.
Consider a state of the system, described by the single particle states ..., n < sub > N </ sub >.
Consider a binary electrolyte AB which dissociates into A + and B-ions and the equilibrium state is represented by the equation:
Consider, for example, the claim that the extinction of the dinosaurs was probably caused by a large meteorite hitting the earth.
Consider two ISPs, A and B, which each have a presence in New York, connected by a fast link with latency 5 ms ; and which each have a presence in London connected by a 5 ms link.
* Chapter 7 divides humility into twelve degrees, or steps in the ladder that leads to heaven :( 1 ) Fear God ; ( 2 ) Substitute one's will to the will of God ; ( 3 ) Be obedient to one's superior ; ( 4 ) Be patient amid hardships ; ( 5 ) Confess one's sins ; ( 6 ) Accept oneself as a " worthless workman "; ( 7 ) Consider oneself " inferior to all "; ( 8 ) Follow examples set by superiors ; ( 9 ) Do not speak until spoken to ; ( 10 ) Do not laugh ; ( 11 ) Speak simply and modestly ; and ( 12 ) Be humble in bodily posture.
Consider three things being pulled by the moon: the oceans nearest the moon, the solid earth, and the oceans farthest from the moon.
Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆ r be the ( relatively small ) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆ r, then the new particle considered may be located on its surface, at a distance ( R ± ∆ r ) from the centre of the sphere of mass M, and ∆ r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of ms own mass, we have the acceleration on the particle due to gravitational force towards M as:
Consider the first claim, that God is a spirit, by itself.
Consider the following URL as it would be requested by a client:
Consider the algorithm described by the pseudocode:
Consider how the vertical and horizontal displacements of the dot, relative to the center of the circle, vary sinusoidally in time and are out of phase by one quarter of a cycle.
Consider " Oh that I had a Thousand Voices " (" O daß ich tausend Zungen hätte ") by German, Johann Mentzer Verse 2: " Ye forest leaves so green and tender, that dance for joy in summer air …" or " O Day Full of Grace " (" Den signede Dag ") by Dane, Nikolai Grundtvig verse 3: " Yea were every tree endowed with speech and every leaflet singing …".
Consider a sample space generated by two random variables and.

Consider and adding
Consider the non-convex polygon P shown in the figure, which is formed from a regular hexagon by adding projections on two of its sides and matching indentations on three sides.
Consider the expansion of to, a maximally imperfect graph, in the sense that is a spanning subgraph of but adding an edge to will result in a perfect matching.
Consider adding < nowiki ></ nowiki > to your user page instead.
Consider forming a permutation of n + 1 objects from a permutation of n objects by adding a distinguished object.
Consider adding this template to pages falling in this category by adding < nowiki ></ nowiki >.

Consider and new
Designer Anthony Ward created a new cobblestone effect for the entire stage while the orchestrations were expanded with new dance arrangements given to Consider Yourself and Who Will Buy?
Consider a system where the gun and shooter have a combined mass M and the bullet has a mass m. When the gun is fired, the two systems move away from one another with new velocities V and v respectively.
* Consider opportunities to introduce new and more renewable energy sources and increase the use of biomass fuels to reduce emissions of carbon dioxide.
Consider a toy model in which a new boson S may couple both to the electron as well as the tau via the term

Consider and constant
Consider a linear differential equation with constant coefficients
Consider N systems in adiabatic isolation from the rest of the universe, i. e. no heat exchange is possible outside of these N systems, all of which have a constant volume and composition, and which can only exchange heat with one another.
Consider a constant time equatorial slice through the Schwarzschild solution ( θ
Consider a population at harvested at a constant harvest level.
Consider an-dimensional space, foliated as a product by subspaces consisting of points whose first co-ordinates are constant.
Consider two equal bodies ( not affected by gravity ), each of mass, m, attached to three springs, each with spring constant, k. They are attached in the following manner:
Consider for example any compact connected complex manifold M: any holomorphic function on it is locally constant by Liouville's theorem.
Consider a complex scalar field φ, with the constraint that φ < sup >*</ sup > φ = v², a constant.
Consider the Laurent expansion at all such z and subtract off the singular part: we are left with a function on the Riemann sphere with values in C, which by Liouville's theorem is constant.
Consider the linear differential equation with a constant w. Its exact basis solutions are and.
Consider a linear differential operator with constant coefficients,
Consider the simplified case of a vehicle with constant mass accelerating vertically upwards with a constant thrust per unit mass a in a gravitational field of strength g. The actual acceleration of the craft is a-g and it is using delta-v at a rate of a per unit time.
Consider that the thermally current-limited components of a large semiconductor inverter are solid-state switches massing a few grams with a thermal time constant to their heat sinks of likely more than 100 ms, whereas the thermally current limited components of an MG are copper windings massing some hundreds of kilos which are intrinsically attached to their own large thermal mass.
Consider a unit circle in, shrinking in on itself at a constant rate, i. e. each point on the boundary of the circle moves along its inwards pointing normal at some fixed speed.
Consider a received discrete signal,, of independent samples that consists of an unknown constant with additive white Gaussian noise ( AWGN ) with known variance ( i. e., ).
The extension of the field to the interior of the ball is not unique ; the need that the physics be independent of the extension imposes a quanitization condition on the coupling constant k. Consider two different extensions of γ to the interior of the ball.
Consider the following expressions from first order logic over a signature containing a constant symbol 0 for the number 0, a unary function symbol s for the successor function and a binary function symbol + for addition.
Consider the linear constant coefficient inhomogeneous system
Consider for example a Hookean spring with spring constant whose dynamics is highly overdamped

0.620 seconds.