You first prove that there are points in space such that, if P is one of them, not more than a finite number of pairs of boots are such that each centre of mass of the two members of a pair is equidistant from P.
There may be a finite number of pairs left over, but they can be dealt with arbitrarily.
Another form of this tendency is shown by Kronecker, Borel, Poincare, and many other mathematicians, who refuse mere logical determination of a conception and require that it be actually described in a finite number of terms.
Before explaining how this occurred, however, it is necessary to say one word in explanation of the phrase "finite number.
This class of functions includes all those which have a finite number of maxima and minima in a finite-interval, and some which have an infinite number.
Since a twisted cubic can be made to satisfy twelve conditions, it might be supposed that a finite number could be drawn to touch four given lines, but this is not the case.
In other words, diffusion is that relative motion of the molecules of two different substances by which the proportions of the molecules in any region containing a finite number of molecules are changed.
This is the third degree of generality, to which we rise, for instance, when we seek to find the most probable law in conformity with a finite number of observations.
By the combination and repetition of a finite number of geometrical operations such as displacements, projective transformations, inversions, &c.
All functions (or rather expressions) which can be made up from those in the table by a finite number of operations of addition, subtraction, multiplication or division can be differentiated by the formal rules.
The indefinite integrals of certain classes of functions can be expressed by means of a finite number of operations of addition or multiplication in terms of the so-called "elementary" functions.
The above list will hopefully provide you with a few useful examples demonstrating the appropriate usage of "finite number" in a variety of sentences. We hope that you will now be able to make sentences using this group of words.
