## Integer Sentence Examples

- Is less than 2 o o If the numerator of the fraction consists of an
**integer**and 4 - e.g. - In the case of a recurring continued fraction which represents N, where N is an
**integer**, if n is the number of partial quotients in the recurring cycle, and pnr/gnr the nr th convergent, then p 2 nr - Ng2nr = (- I) nr, whence, if n is odd, integral solutions of the indeterminate equation x 2 - Ny 2 = I (the so-called Pellian equation) can be found. - These works possess considerable originality, and contain many new improvements in algebraic notation; the unknown (res) is denoted by a small circle, in which he places an
**integer**corresponding to the power. - If we wish to be more general, while still adhering to Deslandres' law as a correct representation of the frequencies when s is small, we may write n - A (s+ 1 1) 2 - - a Po+Pi(s + c) -F +pr(s+ c)r' where s as before represents the
**integer**numbers and the other quantities involved are constants. - For the application of continued fractions to the problem " To find the fraction, whose denominator does not exceed a given
**integer**D, which shall most closely approximate (by excess or defect, as may be assigned) to a given number commensurable or incommensurable," the reader is referred to G. - Comparison with the table of binomial coefficients in ï¿½ 43 suggests that, if m is any positive
**integer**, (I +x)-m =Sr+Rr (25), where Sr=I -m[1]x+m[2]x2...+(-)rm[r]xr (26), Rr_(_)r+1xr+11m[r] (1Fx) - 1+(m - I[r](I+x) m) (27). - The application of the method to the calculation of (I +x) n, when n= p/q, q being a positive
**integer**and p a positive or negative**integer**, involves, as in the case where n is a negative**integer**, the separate consideration of the form of the coefficients b 1, b 2, ... - (v.) Since (r) is an
**integer**, (r) is divisible by r!; i.e. - R= io, we get the ordinary expression of P/Q as an
**integer**and a decimal; but, if P/Q were equal to 1/3, we could not express it as a decimal with a finite number of figures. - If, out of every N cases, where N may be a very large number, a is A in pN cases and not-A in (I - p) N cases, where p is a fraction such that pN is an
**integer**, then p is the probability or frequency of occurrence of A. - He extended the "law of continuity" as stated by Johannes Kepler; regarded the denominators of fractions as powers with negative exponents; and deduced from the quadrature of the parabola y=xm, where m is a positive
**integer**, the area of the curves when m is negative or fractional. - The explanation of this property of the base io is evident, for a change in the position of the decimal points amounts to multiplication or division by some power of 10, and this corresponds to the addition or subtraction of some
**integer**in the case of the logarithm, the mantissa therefore remaining intact. - N's N (I +µ) (s+o.)2 Here and N are constants, while s as before is an
**integer**number. - The pth root of a number (§43) may, if the number is an
**integer**, be found by expressing it in terms of its prime factors; or, if it is not an**integer**, by expressing it as a fraction in its lowest terms, and finding the pth roots of the numerator and of the denominator separately. - The method of electrical images will enable the stream function, )' to be inferred from a distribution of doublets, finite in number when the surface is composed of two spheres intersecting at an angle 7r/m, where m is an
**integer**(R. - An im 5 proper fraction is therefore equal either to an 2 I
**integer**or to a mixed number. - (ii.) To continue the division we may take as our new unit a submultiple of Q, such as Q/r, where r is an
**integer**, and repeat the process. - Trunk series: t N = [s +al +b/s 1 [1 5 +a1 +b'/(I.5)2}2 Main Branch Series: t ytr' - I I N [2 + al + 6/29 2 [r+al Side Branch Series: t nT = N [2 +al+6,/22]2 [s+c+d,s92 Here s stands for an
**integer**number beginning with 2 for the trunk and 3 for the main branch, and r represents the succession of numbers 1 5, 5, 3 5, &c. As Ritz points out, the first two equations appear only to be particular cases of the form n I I N +1)2 in which s and r have the form given above.