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| The number line is occupied by infinitely many numbers.
Fortunately, neither theoretical nor applied mathematics absolutely require that all occupants of the
number line be known. Instead, mathematicians are mostly interested in the characteristic groupings of
numbers. Occupants of the number line are generally known as real numbers.
In some areas of advance mathematics, real numbers are considered to be a subset of the group of
numbers called complex numbers. Complex numbers are generally represented as
a + bi, where a and b are real numbers and i is an imaginary number whose value equals (-1)1/2.
Real numbers consists of rational numbers and
irrational numbers. Rational numbers consists of
whole numbers, fractions and the sums and differences of
whole numbers and fractions. Counting, the concept that initialized the primitive number line, was inspired by the concept of whole quantities. So, it is not surprising that whole numbers are dominant occupants of the number line. Positive Integers (also called natural numbers), 0 and negative integers are all whole numbers. The popular even numbers and prime numbers are also whole numbers. Fractions represent parts of a whole. They occupy the space between 0 and 1, and the space between 0 and -1. |
| In general, rational numbers are represented as the ratio a/b
where a (the numerator or dividend) and b (the denominator or divisor) are whole numbers not equal to zero. If b > a, the rational number is a fraction. If we represent the result or quotient
of a/b by q, then a = bq + r, where r is the remainder after b divides a. If r = 0,
a is called a multiple of b or q and b is called a factor or divisor of a.
If q is not equal to 1 or -1, b is called a proper divisor of a.
If b = 2 and r = 0, a is an even number. If b = 2 and r = 1, a is an odd number .
A prime number is an odd number divisible only by itself and 1. Every integer > 1 can be expressed as a unique product of
prime numbers (repetitions allowed). This statement is known as the fundamental theorem of arithmetic. A perfect number
is a positive integer that is equal to the sum of all its positive proper divisor. For example, 28 =1 + 2 + 4 + 7 + 14. Irrational numbers cannot be expressed as ratios of two whole numbers. They include the square root of 2 ( 21/2), the mathematical constants pi (3.14159265...) and e (2.71828182...), the square root of numbers that are not perfect squares (a number equal to another number raised to power 2) and the cube root of numbers that are not perfect cubes (a number equal to another number raised to power 3). Peter O. Sagay |
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| Let us use our environment respectfully so that future generations would not label us"prodigal ancestors" |
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