The sum, difference, product, or quotient of two rational numbers is always a rational number. Division of any number by zero, however, is not allowed. It can be shown that every rational number can be represented as a repeating or periodic decimal, that is, as a number in the decimal notation, which after a certain point consists of the infinite repetition of a finite block of digits. Conversely, every repeating decimal represents a rational number. Thus, 617/50 = 12.34000 ..., and 2317/990 = 2.34040 ... The first expression is usually written as 12.34, omitting the infinite repetition of the block consisting of the single digit 0. The second expression is frequently written as to indicate that the block of two digits, 4 and 0, is repeated infinitely. The first type of expression is called a finite or terminating decimal, and the second type of expression is called an infinite periodic or repeating decimal (the term infinite is frequently omitted).
Imaginary numbers (the term must not be used in a literal sense but in the technical sense just described) are extremely useful in the theory of alternating currents and many other branches of physics and natural science.
Whereas real numbers represent points on a line, complex numbers can be placed in correspondence with the points on a plane. To represent the complex number a + bi geometrically, the x-axis is used as the axis of the real number a, and the y-axis serves as the axis of the pure imaginary bi; the complex number, therefore, corresponds to the point P with the rectangular coordinates a and b. The line, or vector, joining the origin with the point P (a,b) is the diagonal of a rectangle with the sides a and bi.
If the complex number a + bi is multiplied by -1, the vector OP is
rotated through 180 degrees, and the point P falls in the third
quadrant; a rotation of 90 degrees, therefore, represents
multiplication of the complex number by i, as -1 = 1, and i(a + bi)
represents a point in the second quadrant if a + bi represents a point
in the first.
Mystical and magical qualities have been ascribed to numbers both in
antiquity and in modern times. The pseudoscience of numerology
attempts to interpret the occult by means of the symbolism of
numbers, which is based on the Pythagorean doctrine that all things
are numbers and consist of geometrical figures in various patterns.
Fun Facts about the number Four:
Mystical and magical qualities have been ascribed to numbers both in antiquity and in modern times. The pseudoscience of numerology attempts to interpret the occult by means of the symbolism of numbers, which is based on the Pythagorean doctrine that all things are numbers and consist of geometrical figures in various patterns.