A valid number is a positive number, negative number or zero. All valid numbers are divided into rational and irrational. The first is the number, expressed as a fraction. The second is a real number that is not rational.The set of real numbers has several properties. First, the property of orderliness. It means that any two a valid number only satisfy one of the relations: xy.Second, properties of operations addition. For any pair of real numbers defined by a single number, called their sum. For her, the following relationships: x+y=x+y (the commutative property) x+(y+C)=(x+y)+C (associativity property). If a valid number to add a zero get itself a real number, i.e. x+0=x. If the real number add the opposite of the actual number (-x), we obtain zero, i.e. x+ (-x) = 0.Third, the properties of multiplication. For any pair of real numbers defined by a single number called their product. For him, the following relations: x*y=x*y (the commutative property) x*(y*c)=(x*y)*c (associativity property). If you multiply any real number and a unit, you get a very real number, i.e. x*1=y. If any real number not equal to zero, multiply by a reverse number (1/y), you get a unit, i.e. y*(1/y)=1.Fourthly, the property of distributivity of multiplication relative to addition. For any three real numbers is performed the ratio C*(x+y) = x*C + y*s. fifth, the Archimedean property. Whatever the actual number, there is such an integer that is greater than him, i.e. n>x. The set of elements satisfying the above properties, is an ordered Archimedean field.
What is the actual number
The emergence of the concept of valid numbers due to the practical use of mathematics to Express with a certain number of values of any magnitude, and also the internal extension of mathematics.
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