Alternatively, if characters ' attribute ranks are close, the weaker character can try to change the relevant attribute by changing the nature of the conflict.

Alternatively, if the boards are pre-dealt, " curtain cards " may be supplied which have each hand printed on them, so that each player can check at the beginning of the deal that he has the right cards.

Alternatively, if a line is constructed perpendicularly between Alpha Centauri and Beta Centauri, the point where the above mentioned line and this line intersect marks the Southern Celestial Pole.

Alternatively, if Bishop Cellach was appointed by Giric, it may be that the gathering was intended to heal a rift between king and church.

Alternatively, if using more than one or two techniques for every experiment is infeasible, some of the benefits of consilience may still be obtained if it is well-established that these techniques usually give the same result.

Alternatively, if positive pressures are required, standard glassware can not be used, energy must be used for pressurization and there is a higher chance of side reactions occurring in the distillation, such as decomposition, due to the higher temperatures required to effect boiling.

Alternatively, two figures are congruent if one can be moved on top of the other so that it matches up with it exactly.

Alternatively, 5 ml from a neutron star of radius 20 km radius ( average density ) has a mass of about 400 million metric tons, or about the mass of all humans .</ ref > The resulting force of gravity is so strong that if an object were to fall from a height of one meter it would only take one microsecond to hit the surface of the neutron star, and would do so at around 2000 kilometers per second, or 7. 2 million kilometers per hour.

Alternatively, if the two waves of the same wavelength and frequency are out of phase, then the wave crests will align with wave troughs and vice-versa.

Alternatively, if the last step is carried out in air:

( Alternatively, for a preorder "", a relation "<" can be defined as a < b if and only if ( a b and a ≠ b ).

Alternatively, if several different minerals can be dated from the same sample and are assumed to be formed by the same event and were in equilibrium with the reservoir when they formed, they should form an isochron.

Alternatively, if M is a linear subspace then ; apply this inequality to the subspace defined by the ( orthogonal ) complement of the image of BC in the image of B, whose dimension is ; its image under A has dimension

Alternatively, if the excited-state atom is perturbed by an electric field of frequency, it may emit an additional photon of the same frequency and in phase, thus augmenting the external field, leaving the atom in the lower energy state.

Alternatively, since expendable multistage rockets entail discarding costly structure and engines, if the stages could be reused, this could permit much cheaper operation since the parts costs would be amortized over many flights.

Alternatively, if a predatory ancestor already flying and therefore with long forelimbs, used them to capture prey, it could be pulled on to a predatory foot claw, later inherited and demonstrated by the fighting Velociraptor.

Alternatively, if,, and are known, but is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of, using Kirchhoff's circuit laws ( also known as Kirchhoff's rules ).

Alternatively, if we want to have reasonable discussion we may be practically forced to accept Occam's razor in the same way we are simply forced to accept the laws of thought and inductive reasoning ( given the problem of induction ).

Alternatively, if the magma is erupted it forms volcanic rocks such as basalt, andesite and rhyolite ( the extrusive equivalents of gabbro, diorite and granite, respectively ).

Alternatively, if a strip with an even number of half-twists is cut in half along its length, it will result in two linked strips, each with the same number of twists as the original.

Alternatively, if the data matches the machine address, the data is accepted.

Alternatively, some agree that negative rights may be violated by a government action, but argue that it is justifiable if the positive rights protected outweigh the negative rights lost.

Alternatively, if is discrete, one can construct as the set of all ultrafilters on, with a topology known as Stone topology.

Alternatively, it is possible to show that any bridgeless bipartite planar graph with n vertices and m edges has by combining the Euler formula ( where f is the number of faces of a planar embedding ) with the observation that the number of faces is at most half the number of edges ( because each face has at least four edges and each edge belongs to exactly two faces ).

Alternatively, the difference between points can be used instead of evaluating f ( x, y ) at midpoints.

Alternatively in terms of free current, the line integral of the magnetic H-field ( in ampere per metre, Am < sup >− 1 </ sup >) around closed curve C equals the free current I < sub > f, enc </ sub > through a surface S:

Alternatively, we can keep the same conclusion as in the classical IVT — a single c such that f ( c ) is exactly zero — while strengthening the conditions on f.

Alternatively, where each disc has a radius of f ( x ), the discs approach perfect cylinders as their height dx approaches zero.

Alternatively, posters often replace certain letters with an asterisk, creating " f * ck ", " f ** k ", " f ***" and so on.

Alternatively a therm is used representing 100, 000 or 10 < sup > 5 </ sup > Btu, and a quad as 10 < sup > 15 </ sup > Btu.

Alternatively, it follows from () that if the polar coordinates of the point p are ( r < sub > 1 </ sub >, θ < sub > 1 </ sub >) and those of q are ( r < sub > 2 </ sub >, θ < sub > 2 </ sub >), then the distance between the points is

Alternatively, an analytic function is an infinitely differentiable function such that the Taylor series at any point x < sub > 0 </ sub > in its domain

Alternatively, the mother may prefer to be known as " The Dowager Lady < Bloggs >".

Alternatively, linear independence can be directly defined as follows: a set of vectors is linearly independent if and only if the only representations of the zero vector as linear combinations of its elements are trivial solutions, i. e., whenever a < sub > 1 </ sub >, a < sub > 2 </ sub >, ..., a < sub > n </ sub > are scalars such that

Alternatively a dilute solution of ammonium fluoride ( NH < sub > 4 </ sub > F ) can be used.

Alternatively, the energy source can be another chemical gradient already in place, as in the Ca < sup > 2 +</ sup >/ Na < sup >+</ sup > antiporter.

Alternatively, the right-hand side expression can be justified by multiplying the power series on the left by 1 − x, and checking that the result is the constant power series 1, in other words that all coefficients except the one of x < sup > 0 </ sup > vanish.

Alternatively, some materials with the formula MTiO < sub > 3 </ sub > crystallize in the motif known as Perovskite ( structure ), which is also the name of the mineral form of calcium titanate ( CaTiO < sub > 3 </ sub >).

Alternatively, one can work entirely in a local coordinate system ( x < sup > 1 </ sup >, ..., x < sup > n </ sup >).

Alternatively, an uncountable cardinal κ is supercompact if for every A such that | A | ≥ κ there exists a normal measure over < sup >< κ </ sup >.

Alternatively, a Jordan curve is the image of a continuous map φ: → R < sup > 2 </ sup > such that φ ( 0 ) = φ ( 1 ) and the restriction of φ to