## Integers Sentence Examples

- There was, however, no development in the direction of decimals in the modern sense, and the Arabs, by whom the Hindu notation of
**integers**was brought to Europe, mainly used the sexagesimal division in the ' " "' notation. - (1) he saw that a point or separatrix was quite enough to separate
**integers**from decimals, and that no signs to indicate primes, seconds, &c., were required; (2) he used ciphers after the decimal point and preceding the first significant figure; and (3) he had no objection to a decimal standing by itself without any integer. - Similarly, the other rational
**integers**must be distinguished from the corresponding cardinals. - The orders of the quantic and covariant, and the degree and weight of the leading coefficient; calling these 'n, e,' 0, w respectively we can see that they are not independent
**integers**, but that they are invariably connected by a certain relation n9 -2w = e. - There Is A Still More General Form Of Seminvariant; We May Have Instead Of 0, 0 Any Collections Of Nonunitary
**Integers**Not Exceeding 0, 0 In Magnitude Respectively, (2 A2 3 A3 ...0 Ae)A(L S 2 G2 3 G3 ...0' Ge') B (12 A2 3 A3 ..0 Ab)A(1 S I 2 G2 3 G3 ...B Ge) B (1 22A23A3 ...0 Ae) A(1822 G2 3 G3 ...0' Ge ') B () 8 (1 8 2 A2 3 A3 ...19'°) A(2 G2 3 G3 ...0' ' ') B, Is A Seminvariant; And Since These Forms Are Clearly Enumerated By 1 Z. - (iv.) If P and Q can be expressed in the forms pL and qL, where p and q are
**integers**, R will be equal to (p-kq)L, which is both less than pL and less than qL. - The product of any r consecutive
**integers**is divisible by r! - (b) Let us assume that the product of every set of p consecutive
**integers**is divisible by p!, and let us try to prove that the product of every set of p+ I consecutive**integers**is divisible by (p+i)!. - Do not involve x, and the indices of the powers of x are all positive
**integers**, is called a rational integral function of x of degree n. - Taking any number n to be represented by a point on a line at distance nL from a fixed point 0, where L is a unit of length, we start with a series of points representing the
**integers**I, 2, 3,. - Decimal or Briggian Antilogarithms. - In the ordinary tables of logarithms the natural numbers are all
**integers**, while the logarithms tabulated are incommensurable. - Be
**integers**, a l ib i, a 2 /b 2,. - The point separating the
**integers**from the decimal fractions seems to be the invention of Bartholomaeus Pitiscus, in whose trigonometrical tables (1612) it occurs and it was accepted by John Napier in his logarithmic papers (1614 and 1619). - Are all positive
**integers**, is called a simple continued f raction. - It is evident that, in this case, P ' p2, are two series of positive
**integers**increasing without limit if the fraction does not terminate. - Lagrange used simple continued fractions to approximate to the solutions of numerical equations; thus, if an equation has a root between two
**integers**a and a+1, put x=a+I/y and form the equation in y; if the equation in y has a root between b and b+i, put y = b + I /z, and so on. - The solution in
**integers**of the indeterminate equation ax+by=c may be effected by means of continued fractions. - If we take aq-bp= +1 we have a general solution in
**integers**of ax+by=c, viz. - Two cases have been given by Legendre as follows: If a2, a 31 ..., a n, b 2, b3, .., b n are all positive
**integers**, then I. - - Addition, multiplication and involution are direct processes; and, if we start with positive
**integers**, we continue with positive**integers**throughout. - - A fraction (or fractional number), the numerator or denominator of which is a fractional number, is called a complex fraction (or fractional number), to distinguish it from a simple fraction, which is a fraction having
**integers**for numerator and denominator. - Are
**integers**, and a is an integer or zero. - With
**integers**, besides adding and subtracting, it was easy to double and to multiply by 10: - Law of If we know the weights a and b of two elements that are reciprocal found in union with unit weight of a third element, then proporwe can predict the composition of the compounds which the first two elements can form with each other; either the weights a and b will combine exactly, or if not, these weights must be multiplied by
**integers**to obtain the composition of a compound.