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.