concept of the number refers to the abstraction that characterizes an object from a quantitative point of view.Even in primitive society, people have created a need for counting, so there were numerical designations.Later they became the basis of mathematics as a science.
to handle mathematical concepts, it is necessary, first of all, to present, what are the number.Basic kinds of numbers somewhat.It:
1. Natural - the ones we get in the numbering of objects (their natural account).They represent the set of the Latin letter N.
2. Whole (a lot of them marked with the letter Z).These include natural, opposing them negative integers and zero.
3. Rational numbers (the letter Q).These are the ones that may be represented as a fraction, the numerator of which is equal to an integer, and the denominator - natural.All integers and natural numbers are rational.
4. Actual (they are denoted by the letter R).These include the rational and irrational numbers.Irrationality is a number derived from the rational way of various operations (calculation of the logarithm, root extract) themselves are not rational.
Thus, any of the following sets is a subset of the following activities.An illustration of this thesis is a diagram in the form m. N.Euler diagram.Figure is a plurality of concentric ovals, each of which is located inside the other.Inside, the smallest size oval (area) is the set of natural numbers.It completely surrounds and includes the area that symbolizes the set of integers, which, in turn, lies within the domain of rational numbers.Outside, the biggest oval, which includes all the others, represents an array of real numbers.
In this article we consider the set of rational numbers, their properties and features.As already mentioned, they include all the existing numbers (positive and negative, and zero).Rational numbers constitute an infinite series, which has the following properties:
- this set is ordered, that is, taking any pair of numbers in this series, we can always know which is the greater;
- taking any pair of these numbers, we can always put between them at least one more, and, consequently, a number of those - so rational numbers are an infinite number;
- all four arithmetic operations on such numbers may be, they are always the result of a certain number (and rational);with the exception of division by 0 (zero) - it is impossible;
- any rational number can be represented as a decimal fraction.These fractions can be either finite or infinite periodic.
To compare two numbers belonging to the set of rational, it must be remembered:
- any positive number greater than zero;
- any negative number is always less than zero;
- when comparing the two negative rational numbers more than one of them, whose absolute value (modulus) of less.
How are operations with rational numbers?
To add two numbers with the same sign, it is necessary to lay down their absolute values and put in front of the sum of the total mark.To add numbers with different signs to be of greater value to subtract less and put the sign of them, whose absolute value is greater.
To subtract one number from another rational enough to add to the number of first opposite second.To multiply the two numbers you need to multiply the value of their absolute values.The result will be positive if the factors have the same sign, and negative if different.
division is made similarly to that is private is the absolute values, and the result is placed in front of "+" sign in the case of coincidence of signs dividend and divisor, and the sign "-" in case of a mismatch.
degrees of rational numbers look like the product of several factors that are equal to each other.
