Consider the vectors ( functions ) f and g defined by f ( t ) := e < sup > it </ sup > and g ( t ) := e < sup >− it </ sup >.

Consider the vectors ( polynomials ) p < sub > 1 </ sub > := 1, p < sub > 2 </ sub > := x + 1, and p < sub > 3 </ sub > := x < sup > 2 </ sup > + x + 1.

The first of these three identities says that the 0 form a representation of the ordinary Lie algebra spanned by E ( Consider the 0 as vectors on which the E act.

Consider a discrete charge distribution consisting of N point charges q < sub > i </ sub > with position vectors r < sub > i </ sub >.

Consider the linear subspace of the n-dimensional Euclidean space R < sup > n </ sup > that is spanned by a collection of linearly independent vectors

Fundamental group: Consider the category of pointed topological spaces, i. e. topological spaces with distinguished points.

Consider for example determining which of the following are to be considered diseases ( i. e., abnormal states requiring cure ): alcoholism, homosexuality, and chronic fatigue syndrome.

Consider some set P and a binary relation ≤ on P. Then ≤ is a preorder, or quasiorder, if it is reflexive and transitive, i. e., for all a, b and c in P, we have that:

Consider a space ship traveling from Earth to the nearest star system outside of our solar system: a distance years away, at a speed ( i. e., 80 percent of the speed of light ).

That means that some member of P ( S ), i. e., some subset of S, is not in the image of f. Consider the set:

Consider a loop accessing locations in an equidistant pattern, i. e. the path in the spatial-temporal coordinate space is a dotted line.

Consider the electron ( mass m < sub > e </ sub >) and proton ( mass m < sub > p </ sub >) in the hydrogen atom.

Consider a rigid regular, crystalline, i. e. not amorphous, lattice composed of N particles.

Consider the variance formula: e = PQ, wherein P is equal to the proportion of " 1's " or " cases " and Q is equal to ( 1-P ), the proportion of " 0's " or " noncases " in the distribution.

Consider the question of whether a tossed coin is fair ( i. e. that on average it lands heads up 50 % of the time ).

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 the output across the capacitor at high frequency i. e.

Consider the output across the resistor at low frequency i. e.,

Consider an experiment to study the effect of three different levels of a factor on a response ( e. g. three levels of a fertilizer on plant growth ).

Consider a large group of items in which a very few are different in a particular way ( for e. g. Defective products or infected test subjects ).

Consider a case of a level sensing platform on an aircraft flying due North with its three gimbal axes mutually perpendicular ( i. e., roll, pitch and yaw angles each zero ).

Consider e. g. " A differs from B ".

Consider gas in a one-dimensional container ( e. g., a long thin tube ).

Consider the comparison to its RCOOH acid analogue: the chloride ion is an excellent leaving group while the hydroxide is not under normal conditions ; i. e. even weak nucleophiles attack the carbonyl.

Consider the “ production ” of rock lobster where the costs to produce one rock lobster ( i. e. paying for labour, the nets, and the like, and including normal profit ) amount to $ 3.

Consider the following reactions of acetic acid ( CH < sub > 3 </ sub > COOH ), the organic acid that gives vinegar its characteristic taste:

Consider the example ∇ < big >×</ big > < big >×</ big > F.

Consider the example of a coffee cup and a donut ( see < span class =" plainlinks "> this example </ span >).

Consider two systems ; S < sub > 1 </ sub > and S < sub > 2 </ sub > at the same temperature and capable of exchanging particles.

Consider a pseudo random number generator ( PRNG ) function P ( key ) that is uniform on the interval 2 < sup > b </ sup > − 1.

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 the logarithm function: For any fixed base b, the logarithm function log < sub > b </ sub > maps from the positive real numbers R < sup >+</ sup > onto the real numbers R ; formally:

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

Consider a state of the system, described by the single particle states ..., n < sub > N </ sub >.

Consider the context of evaluating each one of a class of events A < sub > 1 </ sub >, A < sub > 2 </ sub >, A < sub > 3 </ sub >,..., A < sub > n </ sub > ( for example, is the occurrence of the event harmful or not ?).

< p > Consider an interesting and revealing incident that occurred during the Quasi War.

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, for example, the difference between strong and weak convergence of functions in the Hilbert space L < sup > 2 </ sup >( R < sup > n </ sup >).

Consider that 700 < 738, yet 700²

Consider an elastic collision in 2 dimensions of any 2 masses m < sub > 1 </ sub > and m < sub > 2 </ sub >, with respective initial velocities u < sub > 1 </ sub > and u < sub > 2 </ sub >

Consider this table: 1.

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

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

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

Consider the closed intervals for all integers k ; there are countably many such intervals, each has measure 1, and their union is the entire real line.

* 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 a jar containing N lottery tickets numbered from 1 through N. If you pick a ticket randomly then you get positive integer n, with probability 1 / N if n ≤ N and with probability zero if n > N. This can be written

* Consider this example: Sarah says, " Out of every 10 apples I gather, 1 is rotten .".

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

Consider what happens if T < sub > 1 </ sub > fails half-way through.